(Adds details from conference call)

By Stephen Nellis and Sonam Rai

July 31 (Reuters) - Apple Inc sales led by the pricey iPhone X pushed quarterly results far beyond Wall Street targets on Tuesday, with subscriptions from App Store, Apple Music and iCloud services bolstering business.

The world's most valuable technology company also forecast revenue above expectations for the fall, when it typically launches new iPhone models, reassuring a nervous tech sector that saw sell-offs last week in Facebook Inc, Twitter Inc and Netflix Inc on concerns about their future growth.

The Cupertino, California company has responded to a plateauing global smartphone market by launching ever-more expensive phones and diversifying into services, prospering even as rival Samsung Electronics Co Ltd missed targets for its flagship Galaxy S9 and China's Huawei Technologies Co Ltd took the No. 2 global smartphone sales spot.

Apple also regained growth in China, where sales rose 19 percent. Sales there fell dramatically in 2016 after Chinese consumers shunned the iPhone 7, whose overall appearance differed little from its predecessor.

And a $20 billion stock buyback in the quarter spurred by sweeping U.S. corporate tax cuts brought Apple's buyback tally this year to a record $43 billion and exceeded the stock market value of almost three-quarters of the companies in the S&P 500.

"The lesson Apple’s management has learned from the iPhone X, is when you sell a smartphone for more than $1,000 you can sell fewer units and still reap the financial benefits," said analyst Thomas Forte from D.A. Davidson & Co.

Shares rose 3.7 percent in extended trade to $197.34, a record high, putting its market capitalization at $954 billion. The stock would need to hit $206.49 for Apple to become the first publicly traded U.S. company to cross the $1 trillion threshold, based on Apple's share count at the end of the quarter. Apple may have reduced its share count since then.

Apple sold 41.3 million iPhones in the fiscal third quarter, half a million less than expected, but the average iPhone selling price topped expectation by $30, hitting $724, according to FactSet. Apple Chief Financial Officer Luca Maestri told Reuters that customers were buying costlier models and the $999 iPhone X was the quarter's best seller.

Apple posted third-quarter revenue of $53.3 billion and profits of $2.34 per share, compared with analyst estimates of $52.3 billion and $2.18 per share, respectively, according to Thomson Reuters I/B/E/S. (Graphic: https://tmsnrt.rs/2LNgw6q)

It also forecast revenue of $60 billion to $62 billion for its fiscal fourth quarter, which will include early sales of soon-to-be-announced phone models, beating the $59.6 billion analysts expected, according to data from Thomson Reuters I/B/E/S.