Shares rose 3 percent after the bell, adding to the about 23 percent gain so far this year.
The company's shares rose about 4% in extended trading on the results, after closing at $125.01 in NY.
Over the past five years, Microsoft CEO Satya Nadella has guided the company's transformation into a cloud computing leader. At present Azure is following Amazon for cloud services, and leads Google's own products and services.
For the third quarter ended March 31, Azure's growth slowed slightly to 73%, down from 76% in the second quarter.
Microsoft's intelligent-cloud unit recorded the biggest growth of the quarter, up some 22 percent from the same period of 2018. Credit Suisse analyst, Michael Nemeroff, estimates Microsoft's cloud revenue could exceed 50 percent of total revenues in four years. Net income was $8.8 billion, or $1.14 a share, compared with an average analyst estimate of $1 a share, according to data compiled by Bloomberg. Microsoft also topped forecasts with $30.6 billion in revenue, a year-over-year increase of 14%.
"During the same call, Amy Hood, senior vice president and CFO, said that for Azure, the company expects "'continued strong growth in our consumption-based business and moderating growth in our per-user business given the increasing size of the installed base".
Revenue from Microsoft's More Personal Computing segment, which consists of Windows, Xbox, Surface devices, and Bing, grew by only 8% YoY during the quarter to $10.7 billion.
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Chart on the top-valued companies as Microsoft hit the trillion-dollar mark on April 25 (13:30 GMT). In the last quarter alone the company's net profits leapt nearly 20% to $8.8 billion.
Operating income was $10.3bn, a rise of 25 per cent from a year ago.
The company once relied on its Windows operating system for much of its revenues, but this now accounts for just 18% of its sales.
The company's value has skyrocketed over the a year ago, thanks in no small part to its cloud services division.
The company's shares rose about 5 percent in pre-market trading Thursday, after closing at $125.01 in NY, bring the company closer to a $1 trillion market valuation. Here, revenue from LinkedIn also increased by 27 percent and the company highlighted that LinkedIn sessions also increased 24 percent.