By Daisuke Wakabayashi 

Apple Inc. surpassed even the most bullish Wall Street expectations for its holiday quarter with an improbable trifecta: selling more iPhones at higher prices--and earning more on each sale.

The Cupertino, Calif., company said it sold 74.5 million iPhones in the quarter, 46% above a year earlier, while lifting the average selling price of the devices by $50 from the prior year. The total equates to more than 34,000 phones an hour, around the clock.

"Demand for iPhone was staggering," Apple Chief Executive Tim Cook told analysts. "This volume is hard to comprehend."

Results were fueled by Apple's two new larger-display phones, the iPhone 6 and iPhone 6 Plus, which made their debut in September, after years in which Apple ceded the large smartphone market to rivals. Apple encountered supply shortages for weeks in traditional strongholds like the U.S., as well as faster-growing markets like China.

Apple had predicted that the new iPhones would prompt many existing customers to upgrade. Mr. Cook said in an interview that Apple also is luring customers from smartphone manufacturers that use Google Inc.'s Android operating system.

"We brought on more new people to iPhone than ever before," Mr. Cook said. "Many of those are switching from Android, and we couldn't be happier about that."

Apple posted net of $18.0 billion for its fiscal first quarter ended Dec. 27, up 38% from $13.1 billion in the same period a year earlier. That is more than 435 of the companies in the S&P 500 index each made in total profits since 2009, according to S&P Capital IQ.

Earnings per share rose more sharply, up 48% to $3.06 from a split-adjusted $2.07, because of Apple's share buyback program. Revenue increased 30% to $74.6 billion from $57.6 billion.

The results soared past analysts' expectations. Analysts polled by Thomson Reuters estimated that Apple would post earnings of $2.60 a share on revenue of $67.7 billion.

Now, the question is whether the strong iPhone 6 and iPhone 6 Plus sales reflected a one-time boost from pent-up demand for a bigger-display phone or whether Apple can maintain momentum with the next batch of iPhones and new products such as the Apple Watch.

Mr. Cook said the company in April plans to start shipping Apple Watch, its first all-new product since the iPad in 2010. He didn't provide more details on the watch, only to say that development is progressing on schedule.

For the quarter ending in March, Apple expects revenue of between $52 billion and $55 billion with a gross margin of between 38.5% and 39.5% of revenue. Analysts had been forecasting revenue for the current quarter of $53.8 billion and a gross margin of 38.7%, according to Thomson Reuters.

Over the past year, Apple shares have surged 40% due in part to expectations of strong demand for the bigger phones.

Apple shares rose about 5.5% in late trading. Its shares were off $3.96 to $109.14 in 4 p.m. Nasdaq trading before disclosing the quarterly results.

Strong iPhone sales helped Apple claw back market share that it gave up to Samsung Electronics Co. in the past three years. Mr. Cook said iPhone supply finally caught up with demand earlier this month, meaning that the company experienced shortages for the entire quarter.

Analysts estimate Samsung shipped 78 million smartphones in the third quarter. It reports fourth-quarter results on Thursday, though the company doesn't disclose smartphone sales.

Apple's average selling price for its iPhone rose to $687 in the quarter compared with $637 in the year-ago period. Consumers typically pay far less because of carrier subsidies tied to service contracts.

The iPhone 6 Plus costs $100 more than Apple's previous high-end model, and Apple is enticing consumers to upgrade to more expensive models with greater memory.

Apple's performance was especially impressive in China, where researcher Canalys estimates it was the top smartphone seller during the quarter. For greater China, which includes Taiwan and Hong Kong, Apple said revenue rose 70% during the quarter, to $16.1 billion. That moved the region close to overtaking Europe as Apple's second-biggest market. Apple said iPhone sales doubled in mainland China even though its newest models didn't reach that country until mid-October.

Apple said its gross margin, a closely watched indicator measuring the percentage of revenue that remains after manufacturing costs, was 39.9% in the December quarter, up from 37.9% a year earlier. In October, Apple had forecast gross margin of between 37.5% and 38.5% for the quarter.

Apple's iPhone sales provided cover for another sluggish quarter for the iPad. Apple said it sold 21.4 million iPads during the December period, down 18% from a year earlier.

On the other hand, sales of its Macintosh personal computers rose 14% over a year earlier to 5.5 million units. It has gained market share consistently against PC rivals in recent quarters. Research firm IDC said industrywide PC shipments declined 2.4% during the fourth quarter. Competing researcher Gartner said quarterly PC shipments rose 1%.

Apple said its mobile payments service got off to strong start. Apple Pay, which allows consumers to wave an iPhone near a wireless reader, accounts for two of every three dollars spent via contactless payments on Visa, MasterCard or American Express, the company said. It didn't break out Apple Pay in its results.

One drag on Apple's results is the strong U.S. dollar. Apple finance chief Luca Maestri called recent currency moves "unprecedented," and said the impact this quarter would be greater than in the December period.

Apple said the dollar's appreciation shaved four percentage points off revenue growth in its last quarter. A strong dollar hurts Apple by making its products more expensive in other currencies and reduces the value of profit when the money is converted to dollars. Microsoft Corp. expects the strong dollar to shave four percentage points off its revenue growth rate in the current quarter.

Write to Daisuke Wakabayashi at Daisuke.Wakabayashi@wsj.com

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