Commercial cloud revenue more than doubled from a year earlier, the company announced Thursday, and online services like Bing and Xbox Live performed well.
The results were hurt by the weak PC market, however, with sales of Microsoft's Windows and Office software both declining. That meant that while sales were strong, profits declined from last year.
In a statement, CEO Satya Nadella talked of "incredible growth across our cloud services."
Revenue for the quarter, ended March 31, came in at $21.7 billion, up 6 percent from a year earlier, Microsoft said. That beat the analyst forecast of $21.1 billion, according to Thomson Reuters.
Earnings were $0.61 per share, down 10 percent from a year earlier but far ahead of the $0.51 analysts had forecast. Microsoft said results would have been significantly better if not for the effects of a strong dollar, which has been affecting most U.S. companies.
Revenue from Microsoft's Device and Consumer segment, which includes Office 365 Consumer, Xbox, Surface and its Lumia phones, climbed 8 percent from the same quarter last year to $9.0 billion.
Commercial revenue, made up of software and services sold to businesses, was up 5 percent, helped by strong growth from Office 365, Azure and Dynamics CRM.
But sales to businesses of Microsoft's Office and Windows software -- two of its most profitable products -- both declined.
The results are a mixed bag for Nadella, showing that his efforts to grow Microsoft's cloud business are paying off but that Microsoft's fortunes remain heavily tied to the health of the PC market.
Nadella has been reshaping Microsoft since he took over from Steve Ballmer a little more than a year ago. One of his biggest moves was making key Office apps like Word and Excel available for free on Android devices.
He's also said that its upcoming Windows 10 will be a free upgrade for many PC users. That should help ensure a big installed base for the new OS, but it's also left investors wondering what the impact will be on Microsoft's earnings.
Executives may address that question in a conference call planned for Thursday afternoon.
Investors were encouraged by the earnings news, pushing Microsoft's stock up 3 percent in trading after hours, to $44.80.
Among other results from last quarter, Surface revenue of $713 million was up 44 percent from last year, Xbox Live usage grew more than 30 percent, and search ad revenue climbed 21 percent, Microsoft said.
But Windows sales were down across the board, as the refresh cycle from XP drew to a close and customers waited for Windows 10 later this year.
Revenue from Windows Pro licenses sold through PC makers fell 19 percent, while non-Pro revenue fell even more sharply, Microsoft said.