Corrected - Apple reports blockbuster quarter as iPhone sales top estimates

(Corrects paragraph 4 to say "more than two-thirds", not "more than three-quarters")

By Narottam Medhora and Stephen Nellis

(Reuters) - Apple Inc reported its first quarterly increase in iPhone sales in a year, powered by strong demand for the latest version of its flagship smartphone, sending the company's shares up more than 3 percent in after-hours trading.

Apple sold 78.29 million iPhones in the first quarter ended Dec. 31, up from 74.78 million last year. Analysts on average had estimated 77.42 million, according to research firm FactSet StreetAccount.

The results, which reflected the first full quarter of iPhone 7 sales, come at a time when global demand for smartphones is slowing and cheaper Android alternatives are flooding the market.

The company is heavily dependent on the success of iPhones, which account for more than two-thirds of its total revenue.

Analysts and investors have already set their sights on Apple's 10th-anniversary iPhone, which is expected to feature better touchscreen technology, wireless charging and a shift to OLED display.

Apple Chief Executive Officer Tim Cook said demand was especially high for the larger iPhone 7 Plus in the first quarter.

Revenue in the services business - which includes the App Store, Apple Pay and iCloud - jumped 18.4 percent to $7.17 billion, helped by the popularity of games, including Pokemon Go and Super Mario Run, and increased revenue from subscriptions.

Analysts expect growth in the segment to help offset declining hardware sales as the smart phone market matures.

Apple Chief Executive Tim Cook said on a conference call on Tuesday that he expects services revenue to double in the next four years.

"Services obviously continues to be a real success story for them. It's one of the fastest-growing segments they have, driven largely by the App Store," said Jackdaw Research analyst Jan Dawson.

Apple's revenue from the Greater China region fell 11.6 percent to $16.23 billion.

"We were encouraged by our performance in China because it was clearly an improvement over the last couple of quarters. In mainland China in particular, our revenue was flat and actually grew in constant currency terms," Chief Financial Officer Luca Maestri said.

The company also forecast revenue of between $51.5 billion and $53.5 billion for the current quarter. Analysts, on average, had expected revenue of $53.79 billion, according to Thomson Reuters I/B/E/S.

Maestri added that a stronger dollar hurt the company's revenue forecast.

Analysts on average expect the company to sell 53.43 million iPhones in the current quarter, according to FactSet.

The company's net income fell to $17.89 billion in the quarter from $18.36 billion a year ago. On a per share basis, it earned $3.36, beating the average analyst estimate of $3.12.

Revenue rose 3.3 percent to $78.35 billion in the quarter, compared with the average estimate of $77.25 billion, according to Thomson Reuters I/B/E/S.

Up to Tuesday's close, Apple's shares have gained about 15 percent since mid-November, compared with the 5.3 percent rise in the Dow Jones Industrial Average .

(Reporting by Narottam Medhora in Bengaluru; Editing by Saumyadeb Chakrabarty)