Last week Microsoft delivered quarterly earnings that beat Wall Street predictions and offered another affirmation of the company’s bet on a cloud-dominated future defined by the “digitization of people, places and things,” as CEO Satya Nadella put it.

Microsoft reported fiscal second-quarter profit of $11.6 billion on revenue of $36.9 billion, representing year-over-year increases of 38% and 14%, respectively. Earnings per share were $1.51, a 40% increase from a year earlier.

In the days leading up to Wednesday’s report, which covered the three months ending Dec. 31, analysts had expected revenue of $35.7 billion and earnings of $1.32 per share, according to Bloomberg.

Microsoft shares closed Wednesday at $168.04, or nearly 58% higher than a year ago, and soared more than 4% in after-hours trading.

Microsoft’s results relied heavily on its cloud-computing businesses. Azure, Microsoft’s cloud-infrastructure service, grew by 62% over the same quarter last year — a pace that exceeds the growth rate for the broader cloud industry, according to Goldman Sachs analyst Heather Bellini. Microsoft’s total cloud revenue was $12.5 billion for the quarter, up 39% from a year earlier.

Microsoft also saw strong revenue growth in its commercial version of Office 365 (27%) and with LinkedIn (24%).

The company’s only real disappointment was in its Xbox division, where quarterly revenue fell 11%. Microsoft said that decline was driven in part by the imminent release of the next Xbox console.

Wednesday’s results show that Microsoft is gaining ground in the battle over the rapidly growing cloud-computing market. Although crosstown rival Amazon remains the industry leader with its Amazon Web Services, Microsoft has scored several big wins recently. Among them are a large cloud contract with KPMG, one of the largest accounting firms, and a $10 billion contract, known as JEDI, to provide cloud services to the U.S. military for the next 10 years.

Analysts were especially impressed with the growth Microsoft continues to see in its cloud business. Amy Hood, Microsoft’s chief financial officer, who joined Nadella on a conference call with analysts Wednesday afternoon, said that growth reflects both the company’s strategy and “just how much revenue opportunity exists in cloud.”

That view is shared by analysts, who expect the cloud business to keep booming as companies, governments and other organizations put more of their data and computing operations onto centralized servers run by Microsoft, Amazon and others.

Because the cloud business remains so profitable, Microsoft and its rivals are rapidly expanding their data centers and developing applications to manage and analyze the data stored in those centers.

“As the business scales, the profitability increases,” Hari Srinivasan, senior research analyst and technology portfolio manager at Neuberger Berman Group, told Bloomberg. “The cloud business is on fire.”