Better in their words…

It was touch and go for a time. Months before the pandemic took hold, she implemented widespread layoffs. To stave off bankruptcy after oil prices collapsed in 2020, she slashed spending and nearly eliminated Occidental’s once-sacrosanct dividend—“the biggest and toughest decision that I made and I’ve ever made in my career,” she said in an interview.

Her 2019 acquisition of rival Anadarko Petroleum Corp., which Mr. Icahn called a “disaster,” has given Occidental the dominant position in the largest U.S. shale-oil field, the Permian Basin. Lifted by climbing oil prices, Occidental generated a record $4.35 billion in free cash flow and $3.7 billion in profit in the second quarter. It has cut its debt to $22 billion from nearly $36 billion a year ago.

Oil-and-gas producers have reported banner profits this year, even as a global energy crisis sparked by Russia’s invasion of Ukraine has threatened to derail European industries, left the U.K. facing its worst economic crisis since the 1970s and forced the Netherlands, Germany and India to rely heavily on coal to make up for a dearth of natural gas.

But Ms. Hollub, the first woman to be CEO of a major U.S. oil company, says she doesn’t feel vindicated. “I just feel relief,” she said. “There were a lot of doubters.”

Mr. Buffett has publicly lauded Ms. Hollub’s leadership. After she detailed the company’s future plans for analysts in February, Mr. Buffett told his own shareholders, “What Vicki Hollub was saying made nothing but sense.” Last month, Berkshire received regulatory approval to buy up to 50% of the oil company’s shares, spurring speculation it might seek to purchase all of Occidental.

On Friday, the conglomerate reported it has bumped its stake in Occidental to 26.8% from a little over 20%, according to regulatory filings.

Mr. Buffett declined to comment for this story. Ms. Hollub said she has “tremendous respect” for Mr. Buffett, adding that “he will be very beneficial for us as we go forward.” She declined to discuss the possibility of Berkshire purchasing the entire company.

Some former investors remain skeptical, saying a spike in oil prices has rescued the company, not Ms. Hollub.

“I have nothing personal against Vicki,” Mr. Icahn said in an interview. “However, that will never change my mind that she should not have made a bet-the-company investment by way of overpaying for Anadarko.”

A University of Alabama graduate, Ms. Hollub joined Occidental in 1982 and soon found herself running operations in Russia and Venezuela. She almost got laid off in 2003, but Todd Stevens, an executive at the company who had followed her rise, arranged for her to lead a team evaluating acreage in Colorado, said Mr. Stevens, who has since left.

Ms. Hollub became known as a hard worker, once spending three weeks straightening out operations at a new gas field’s first well, said Donnie Enns, a former geophysicist who worked under her. “Nobody worked harder than Vicki,” he said. She also found time to run an office March Madness basketball pool.

After being named CEO of the company in 2016, Ms. Hollub departed from her predecessor’s preference for low-risk, “bolt-on” transactions. A little over a year into the job, she started courting Anadarko, an oil producer of comparable size, for a deal.

She outflanked larger Chevron Corp. in a bidding war that riveted the oil patch, offering $5 billion more than her rival for Anadarko and its prized assets in the epicenter of U.S. shale production. Yet victory came at a steep cost.

Some of Occidental’s largest shareholders decried the deal—especially a pricey loan from Mr. Buffett in the form of $10 billion in preferred stock paying 8% annually in dividends, or $800 million. Ms. Hollub negotiated the funding at the eleventh hour after meeting with the financier in Omaha, Neb. Mr. Icahn, who first bought stock as the Anadarko bidding war came to a close, wrote to Occidental shareholders that “Buffett figuratively took her to the cleaners.”

Ms. Hollub acknowledged the deal damaged the company’s standing with some investors. “I was never offended at the fact that our shareholders were skeptical,” she said.

But she said she never doubted the wisdom of the acquisition, even after it sparked an investor revolt that created an opportunity for Mr. Icahn.

Central to Ms. Hollub’s strategy was building on Occidental’s already-large position in the oil-rich Permian of West Texas and New Mexico. She believed purchasing and drilling a huge swath of new acreage, much of it near the company’s existing assets, would give Occidental economies of scale and allow it to outperform Permian rivals. Occidental, she said, was one of the most technologically advanced drillers in the field; it would turn Anadarko’s undeveloped assets into oil-gushing wells.

By the end of 2019, the oil producer said it was making progress on its merger goals. It had divested itself of more than $6 billion in assets, including stakes in a liquefied natural gas export project in Mozambique and in a Houston-based pipeline company. Occidental recorded single-day and monthly production records in the Permian and other oil fields. Occidental announced its 182nd consecutive quarterly dividend, which Ms. Hollub noted at the time that “few other companies can claim.”

Ms. Hollub believed the merger was on track, but investors remained skeptical. From the time of Occidental’s counteroffer for Anadarko in April 2019 to February 2020 Occidental’s stock fell around 35%. Then the global pandemic took hold.

As billions of people around the world began to lock down, demand for oil plummeted. In the spring, oil prices reached historic lows, briefly turning negative for the first time ever as traders paid counterparties to take oil off their hands. Falling demand for their product hammered oil-and-gas companies, forcing dozens into bankruptcy.

Every day, Ms. Hollub would drive to Occidental’s Houston offices in her red Jeep Wrangler, said Glenn Vangolen, a former senior vice president at Occidental and close adviser to the CEO. Mondays and Fridays, she and her lieutenants would mask up and gather in a conference room to discuss operations. Her office was spartan—a mostly bare room, except for a TV playing business news on mute, and a plush stuffed version of a costumed elephant, the Alabama Crimson Tide’s mascot, Mr. Vangolen said.

Occidental was in a worse situation than many of its peers: At the end of 2019, its long-term debt of about $39 billion was equivalent to roughly four times its earnings, excluding interest, taxes and other accounting items, quadruple the ratio from a year earlier, S&P Capital IQ data show. The divestitures it had planned on to pay it down were no longer viable as assets were losing value.

Ms. Hollub said that Occidental made a lot of the difficult decisions before the pandemic to mitigate the downside risks of the Anadarko acquisition, including hedging a portion of its oil production and bumping its line of credit to $5 billion. But the company still faced painful months ahead as it had barely enough cash on hand to meet debt maturities coming due in 2021 and was later forced to hire restructuring advisers.

Ms. Hollub moved to cut her executives’ salaries—including her own by 81%—offer employees voluntary buy-outs, slash expenses in the oil patch and cancel employee perks. She also cut the dividend, which rankled investors.

Mr. Icahn amplified his calls for Ms. Hollub’s ouster and said he would seek to replace the entire board of directors at the company’s annual meeting. As the oil producer’s stock plunged to under $10 from around $45 before the pandemic, Mr. Icahn—facing paper losses of about $1 billion—doubled down on his shares, boosting his stake to roughly 10% from about 2%.

After a price war between Russia and Saudi Arabia caused oil prices to plunge below $25 a barrel in March, Occidental reached a settlement with Mr. Icahn. The deal gave board seats to two of his deputies and added another director, required Occidental to create an oversight committee that must be informed of any offers to acquire the company or its assets, and replaced the board chairman with Stephen Chazen, Ms. Hollub’s predecessor as CEO.

Mr. Icahn’s camp pushed for Occidental to give its shareholders warrants that could allow them to buy discounted shares in the future. After he prevailed, Mr. Icahn received roughly 11 million warrants initially and bought more when they were worth around $3.

Mr. Vangolen said Mr. Icahn’s demand for warrants was part of the investor’s “raider playbook,” which he described as “trying to extract as much cash out of the business as you can before you bail.”

Mr. Icahn said that all the shareholders who rode the stock down deserved something for their loyalty.

As the pandemic dragged on, Occidental logged a roughly $14.8 billion loss for 2020, its largest on record, according to S&P Capital IQ data. Still, it continued to whittle down its mammoth debt, closing around $2.5 billion in asset sales at the end of 2020. Anadarko’s assets, meanwhile, were starting to shine, with production in the Permian reaching the high end of company estimates.

Even as Ms. Hollub wrestled with Mr. Icahn, she was building a relationship with Mr. Buffett.

In 2020, she traveled to Omaha to discuss Occidental’s long-term strategy with Mr. Buffett, according to a person familiar with the meeting. The investor expressed a strong interest in the company’s goal to become a leader in carbon capture, this person said.

Occidental says it has no plans to stop producing oil but also aims to be a leader in “carbon management.” It wants to develop 70 plants by 2035 to suck carbon dioxide out of the air, store it in the ground and sell carbon credits to businesses seeking to offset their own emissions—a technology still in its commercial infancy that received a boost thanks to tax credits included in the climate package President Biden signed into law last month. The company also plans to use the gas to squeeze more oil from underground.

Then, in late February of this year, Russia invaded Ukraine.

The war propelled oil prices to their highest level in years, with Brent crude oil topping $120 in March, translating into a windfall for oil companies. In the first quarter of the year, Occidental made roughly $4.9 billion in profit, its highest quarterly earnings on record, according to S&P Capital IQ.

The company now holds the most acreage across the Permian, with leases covering about 2.8 million net acres, according to data firm Enverus. Its domestic oil output in the second quarter of this year was up roughly 80% compared with before it acquired Anadarko, Occidental reported.

As Occidental’s stock rose above $50 a share in March, Mr. Icahn sold his common stake. The investor’s two representatives on Occidental’s board also resigned, as was required by the settlement agreement. Mr. Icahn made over $1.5 billion on his investment and still holds some warrants, according to public filings and people familiar with the matter.

As Mr. Icahn got out of the stock, Mr. Buffett bought in. In May, Berkshire reported it had purchased roughly $8 billion worth of shares.

Mr. Icahn said that Mr. Buffett’s investment could be ill-timed. “I respect Buffett a lot but I think buying this stock at this level is obviously not like buying warrants at $3,” he said. “I made a great deal of money on my investment in Occidental, especially with the warrants, and activism worked in that regard,” he said.

Ms. Hollub and Mr. Buffett have developed a personal relationship and the two talk periodically, said Mr. Vangolen. Ms. Hollub said in an interview she had no personal relationship with Mr. Icahn when he was an investor, and that he turned out not to be the kind of long-term shareholder the company prizes.

Mr. Icahn’s retort: “She came very close to not being a long-term shareholder also, because her ill-timed investment put the company on the brink of bankruptcy.”

Akane Otani contributed to this article.

Write to Benoît Morenne at benoit.morenne@wsj.com and Cara Lombardo at cara.lombardo@wsj.com