(Adds analyst comments, revenue detail and updates share price)

Oct 20 (Reuters) - Microsoft Corp reported adjusted revenue and profit that blew past analysts' estimates on Thursday, as soaring sales from its cloud business pushed the technology giant's shares to an all-time high.

Microsoft's shares rose 5.8 percent to $60.59 in after-hours trading.

The Redmond, Washington-based company said revenue from its flagship cloud product Azure, which businesses can use to host their websites, apps or data, rose 116 percent.

"There's a huge runway for them to show growth," said Trip Chowdhry, managing director of Global Equities Research, noting the market for cloud services will be controlled almost entirely by Microsoft and larger rival Amazon.com Inc .

Revenue from Microsoft's overall "Intelligent Cloud" business, which sells computer services and storage to corporate customers, rose 8.3 percent to $6.38 billion.

This beat analysts' average estimate of $6.27 billion, according to research firm FactSet StreetAccount.

Cross Research analyst Shannon Cross said, "Microsoft is uniquely positioned for the hybrid cloud world... because they can move (from the) data center all the way up into the public cloud with Azure."

Under Chief Executive Satya Nadella, Microsoft has been focusing on cloud services and mobile applications as growth slows in its traditional software business.

Nadella orchestrated Microsoft's biggest-ever deal, reaching an agreement in June to buy LinkedIn Corp for $26.2 billion.

Worldwide PC shipments fell 3.9 percent in the quarter ended Sept. 30, according to research firm IDC, although that was much less than the 7.1 percent it had previously estimated.

Revenue in the unit that includes Windows software and the company's struggling mobile business fell 1.8 percent to $9.29 billion.

Net income fell to $4.69 billion, or 60 cents per share, from $4.90 billion, or 61 cents per share, a year earlier.

Excluding items, Microsoft earned 76 cents per share, beating analysts' average estimate of 68 cents, according to Thomson Reuters I/B/E/S.

On an adjusted basis, Microsoft reported revenue of $22.33 billion, above the average estimate of $21.71 billion.

(Reporting by Anya George Tharakan in Bengaluru and Jeffrey Dastin in New York; Editing by Don Sebastian, Bernard Orr) ((anyageorge.tharakan@thomsonreuters.com; within U.S. +1-646-223-8780; outside U.S. +91 80 6749 7118;; Reuters Messaging: Reuters Messaging: anyageorge.tharakan.thomsonreuters.com@reuters.net))