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Microsoft Corp.’s push into cloud computing, which is accelerating under new CEO Satya Nadella, paid off in the fiscal third quarter.

Net income in the period that ended March 31 was $5.66 billion, or 68 cents a share, Microsoft said Thursday in a statement.

That topped the average analyst estimate of 63 cents, according to data compiled by Bloomberg. Sales were $20.4 billion, matching projections.

Nadella, who took the helm two months ago, is leading a shift to focus on selling devices and software delivered over the Internet, both for Microsoft’s own Windows operating system and rival programs. Rising sales of Web-based tools, such as Office software and Azure cloud services, are helping the largest software maker grapple with shrinking personal-computer demand and a failure to gain ground in tablets and phones.

“Cloud continues to be a pillar of strength,” said Daniel Ives, an analyst at FBR Capital Markets & Co., who rates the shares the equivalent of a hold. “It’s not a great PC market at all, but it has become less bad.”

Microsoft shares rose as much as 2.9 percent to $41 in extended trading following the report. They advanced less than 1 percent to $39.86 at the close in New York. The stock climbed 9.6 percent last quarter, compared with a 1.3 percent increase in the Standard & Poor’s 500 Index.

Microsoft beat profit estimates by saving money on the costs of running cloud services, as well as marketing, said Chief Financial Officer Amy Hood. Gross margin in the Commercial Other segment, largely cloud products, increased 80 percent.

Microsoft will bolster its smartphone offerings through the acquisition of Nokia Oyj’s device and services business for $7.5 billion, a deal that the companies expect to close today.