Chief executive Satya Nadella has been focusing on cloud services and revenue for the division rose 5% to $6.3bn.
However, profits for the three months to 31 December fell 15% to $5bn (£3.4bn) as the strong dollar and falling PC sales took their toll.
Total revenue also slipped 10.1% to $23.8bn.
Both numbers were better than analysts had expected.
NPD Group analyst Stephen Baker said: "People who think Microsoft is sliding into irrelevancy really need to re-evaluate how they see the company. They are a software-first company in a world that is increasingly about software."
Matt Howard, a venture capitalist at Norwest Ventures, said Microsoft had "nailed the cloud".
Mr Nadella said: "The enterprise cloud opportunity is massive - larger than any market we have ever participated in."
Microsoft's combined cloud business, which also includes other divisions such as Office 365, was on track for $9.4bn in annual revenue - higher than its previous forecast of $8.2bn.
The global cloud storage industry was worth almost $19bn last year, according to Research and Markets. The group estimates that will rise to $65bn by 2020.
Microsoft's decision to focus more on cloud services - where its competitors include Amazon, Google, IBM and Cisco - has helped it move away from the declining PC market.
Microsoft's revenue from personal computing, which includes the Windows business, fell 5% in the quarter to $12.7bn.
Global PC shipments fell 10.6% in the fourth quarter compared with the same period in 2014, according to IDC.
The research firm said PC sales should improve later this year as companies that had delayed replacing computers ahead of the release of Windows 10 last summer start buying again.
Tablet computers were a bright spot for Microsoft, with revenue up 29% following the launch of the Surface Pro 4 and Surface Book.
The number of people using the Xbox Live service for digital content and video games climbed 30% to a record 48 million.
Shares in Microsoft were up 4.2% to $54.25 in after-hours trading in New York and have risen 10% in the past 12 months.
Microsoft shares rose in after-hours trading as it reported strong growth in its cloud computing and mobile applications divisions.