Apple also said iPad sales worldwide nearly doubled from a quarter ago, a sign that it has left the worst of its supply problems behind.
Apple's stock surged nearly 5 percent after the results came out.
Net income in the fiscal third quarter, which ended in June, was $7.31 billion, or $7.79 per share. That's more than double the $3.25 billion, or $3.51 per share, a year ago.
Analysts polled by FactSet were expecting earnings of $5.82 per share.
Revenue was $28.6 billion, up 82 percent from $15.7 billion a year ago. Analysts were expecting $24.8 billion.
The results were lifted by the sale of 20.3 million iPhones, millions more than analysts had expected. The phone's popularity in Asia, particularly in China, is helping. So is the fact that Apple keeps expanding the number of carriers that sell the phone. It was the first full quarter in which the phone was sold by Verizon Wireless, the largest carrier in the U.S. Before, only AT&T sold the phone in the U.S.
Apple usually has the year's new iPhone model out by early July. That hasn't happened this year, and analysts expect the new model to come in September instead. Apple executives didn't provide any specifics on a call with analysts.
Executives also resisted questions on whether Apple will produce a cheaper iPhone to compete against phones powered by Google Inc.'s Android software. Asian competitors like Samsung Electronics, LG Electronics and HTC Corp. are selling tens of millions of Android phones every quarter at prices that undercut the iPhone.
"We will only make products that we are proud of, that are the best in the world. And if we can do that, and the price is lower, then we are great with that," Chief Operating Officer Tim Cook told analysts on the call.
IPad sales came in at 9.25 million units, also above analyst expectations. Last quarter, the company was struggling to make enough of the new iPad 2. Apple has sold nearly 29 million iPads since they first went on sale in April 2010.
In other product categories, trends were less impressive. Sales of Mac computers were 3.95 million, up 14 percent from a year ago. That's the lowest quarterly growth rate in two years.
Cook said some people were probably buying iPads instead of Macs in the quarter, but he said more people were buying iPads over Windows PCs. He said he was pleased with 14 percent growth compared with overall PC market growth of 2.6 percent, as measured by research firm IDC.
Some buyers may also have been holding off while waiting for Lion, the new version of the Mac OS X operating system. Apple had said it would go on sale this month, and Apple confirmed on the call that it will go on sale Wednesday. Lion will cost $29.99 and mimics some of the features of the iPhone and iPad interface.
IPod sales were down 20 percent at 7.5 million, as the music and video players continue to lose out to iPhones and iPads. It was the fastest quarterly decline yet.
Cook is running day-to-day operations while CEO Steve Jobs is on indefinite medical leave. The quarter was the first full one since Jobs went on leave in January. Jobs remains involved in major decisions, including announcements of new products. Analysts don't expect Jobs' leave to affect the company much in the short term. All the company's major products have still been shepherded by Jobs.
Chief Financial Officer Peter Oppenheimer said he expects earnings of $5.50 per share and revenue of $25 billion in the quarter that just started. Both figures point to a decline from the third quarter. However, the company usually lowballs its financial forecasts, and analysts are unlikely to take the forecast seriously.
Apple's stock surged $18, or 4.8 percent, to $394.85 in extended trading after the company announced results late Tuesday. In the regular session, it hit a 52-week high of $378.65, before closing at $376.85, up nearly 1 percent.