The Redmond, Washington based technology giant reported net income of $8.8 billion (roughly Rs. 64,500 crores) on revenue of $29.1 billion (roughly Rs. 2.1 lakh crores) in the quarter that ended on September 30, up 34 percent and 19 percent respectively from the same period a year earlier.
Shares were up 1.6 percent to $104 (roughly Rs. 7,600) in after-market trades that followed release of the earnings figures for the first quarter of its fiscal year.
"We are off to a great start in fiscal 2019, a result of our innovation and the trust customers are placing in us to power their digital transformation," Microsoft chief executive Satya Nadella said in a release.
"We're excited to help our customers build the digital capability they need to thrive and grow."
Nadella has led a transformation at Microsoft from a company focused on software installed on machines in homes and businesses to making money from services hosted on the internet and available from a broad array of devices regardless of who makes them.
"Our record results for Q1 reflect our commitment to long-term strategic investments and consistent execution to drive revenue growth and operating margin expansion," said chief financial officer Amy Hood.
"We see continued demand for our cloud offerings, reflected in our commercial cloud revenue of $8.5 billion, up 47 percent year-over-year."
Money taken in by a productivity and business processes unit rose to $9.8 billion, including strong growth in cloud-based Office productivity products aimed at consumers and companies, according to Microsoft.
LinkedIn revenue grew 33 percent in the quarter, with the career-oriented networking service boasting record levels of engagement by users.
Microsoft's cloud platform Azure, which performs computing and storage for companies at online data centers, saw revenue grow 76 percent.
Azure is part of a Microsoft "Intelligent Cloud" division that, overall, reported revenue up 24 percent to $8.6 billion.
"Microsoft just delivered an eye-popping cloud beat and a performance that speaks to a secular cloud story which is still in the early innings of playing out," Wedbush analysts said in a note.
It appeared that spending by companies on cloud is accelerating, with Microsoft and Amazon in a "two horse race" as leading platforms, according to Wedbush.
Global Equities Research analyst Trip Chowdhry called the Microsoft earnings a "solid beat" of Wall Street expectations, projecting shares could climb to $120.
While money from the Windows unit was up just a few percent, Microsoft chief financial officer Amy Hood said revenue there was expected to improve as consumers and businesses replace older machines with new hardware powered by the latest version of the operating system.
Microsoft, maker of Xbox consoles, also saw revenue from gaming hardware, software and services jump 44 percent.
Nadella said a keenly-anticipated "X Cloud" video game streaming service is in "early days" but he is excited by the prospect of a service that will let players access console-quality titles on all kinds of internet-linked devices.
"Most critical is having a platform where gamers are already there," Nadella said of the project during an earnings call with analysts.
"I am most excited about the core (Xbox) community and content we have; I think that is what even gives us permission to think about streaming."
The company said it returned $6.1 billion (roughly Rs. 44,700 crores) to shareholders during the quarter in the form of dividends or share buy-backs.