Microsoft Corp.’s (MSFT) fiscal first-quarter profit jumped 17%, as its steady pipeline of software sales helped it stay ahead of a shrinking personal-computer industry.

Shares jumped 6.2% to $35.87 in after-hours trading as the company’s results easily topped Wall Street’s expectations.

The Redmond, Wash., software giant continues to churn out big profits, but has missed potential growth areas as people and businesses shift more computing chores to the Web, tablets and smartphones. Adapting the company to those changes soon will fall to a new leader. Steve Ballmer, Microsoft’s chief executive since 2000, announced in August he plans to retire within a year.

Microsoft’s revenue grew 16%, to $18.53 billion, and the figure climbed 7.4% to $18.64 billion on an adjusted basis. Analysts surveyed by Thomson Reuters had projected $17.79 billion in revenue.

Revenue from products sold to consumers, including PCs and the company’s Surface tablet and Xbox videogame systems, grew 4.2%. Software and other services sold to corporations–an area in which Microsoft has a stronger grip–rose 9.8%.

Microsoft is spending more money to market new products like its year-old Windows 8 operating system, and to bolster its computing infrastructure for delivering software and services over the Web. The spending has meant Microsoft’s profits are rising more slowly than its sales.

For the quarter ended Sept. 30, Microsoft reported a profit of $5.24 billion, or 62 cents a share, up from $4.47 billion, or 53 cents a share, a year earlier. Excluding deferred revenue related to Windows sales, adjusted profit fell to 63 cents from 65 cents a year ago. Analysts had been looking for an adjusted profit of 54 cents.

Write to Shira Ovide at shira.ovide@wsj.com and John Kell at john.kell@wsj.com