NEW YORK, United States — After years of Amazon.com Inc. drubbing Wal-Mart Stores Inc. in e-commerce, the brick-and-mortar chain is beginning to push back.

Wal-Mart posted its third straight quarter of double-digit online growth, which helped its holiday results top estimates. The world’s largest retailer is benefiting from last year’s acquisition of Jet.com, a $3.3 billion deal that reinvigorated a flagging e-commerce business and brought a new executive team to the division.

Wal-Mart is finally “playing offence,” said Peter Benedict, an analyst at Baird Equity Research.

Online sales gained 29 percent in the fourth quarter, which ended January 31. The results sent shares up as much as 3.9 percent to $72.07 in early trading on Tuesday.

Amazon remains dominant in the online market, but Wal-Mart is spending billions to catch up. In addition to acquiring Jet.com, the Bentonville, Arkansas-based company agreed to purchase ShoeBuy.com and outdoor e-tailer Moosejaw. Wal-Mart also put Jet.com founder Marc Lore in charge of the online strategy and has scrapped an unsuccessful membership program that mimicked Amazon’s Prime plan.

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Lore used to work at Amazon, which acquired an earlier business of his, Quidsi. And the 45-year-old is seen as a visionary in the field, said Michelle Grant, an analyst at Euromonitor International.

“Marc Lore is the second-smartest person in e-commerce behind Jeff Bezos,” she said. “He relishes the challenge of taking on Amazon.”

Even with Wal-Mart’s recent resurgence, it won’t be an easy battle. Almost three out of four Wal-Mart shoppers bought something on Amazon during the holiday quarter, according to data tracker Prosper Insights & Analytics. That’s up from two-thirds who said the same back in 2014 -- a sign that Wal-Mart has less of a hold on its customers.

“We’re happy about how fast we’re moving, but still have a lot of work to do,” Lore said on a call with reporters, adding that he’s open to doing more acquisitions. He’s looking at opportunities similar to last week’s deal for Moosejaw, which added upmarket brands such as Patagonia.

Wal-Mart’s brick-and-mortar performance was more measured, though it still exceeded analysts’ estimates last quarter. US same-store sales rose 1.8 percent, beating the 1.3 percent prediction. That was the biggest increase in more than four years. Excluding some items, earnings amounted to $1.30 a share. Analysts had estimated $1.29.

Wal-Mart’s holiday numbers contrasted with a downbeat performance at rival Target Corp., which cut its fourth-quarter earnings forecast after sales were hurt by “disappointing” customer traffic. That company will deliver its full results next week.

The industry leaders also are fretting over a possible border-adjusted tax, which they say will force them to raise prices. Retail trade groups have been lobbying against the measure, squaring off against industrial companies that like the idea. Wal-Mart chief financial officer Brett Biggs said that the tax proposal was a concern, but it was too early to discuss possible impacts.

“If import prices increase, at some point it will find its way through the system,” he said.

Wal-Mart expects first-quarter earnings to range between 90 cents and $1 share. Analysts estimate 96 cents. US same-store sales will gain 1 percent to 1.5 percent in the period, the company said.

There’s a risk that Wal-Mart’s online push could detract attention from its physical stores, which are grappling with the longest stretch of food deflation since 1960 and encroachment from discount chains.

Investors have been nervous about Amazon spending too much on the e-commerce expansion, which has weighed on profit. Products sold online also typically have smaller margins. The latest results may help allay concerns about chief executive officer Doug McMillon’s ambitions, Grant said.

“McMillon has been doing decent job of convincing people that it’s worth spending the money in order to be competitive,” she said.

By Matthew Boyle and Molly Smith; editors: Matthew Boyle and Nick Turner.