The firm reported a $13.6bn (£8.9bn) profit, with revenue up 27% to $58bn.
Sales in greater China leapt 71% to $16.8bn, outpacing those in the US for the first time, and helping to drive the sharp profit rise.
Apple also said it would ramp up its share-buying programme, returning $200bn to investors, up from $130bn.
The tech giant said it currently had a record $195bn in cash on its books.
However, sales of its iPad tablet remained sluggish. Apple said it sold 12.6 million iPads, down 23% from a year earlier.
“We are thrilled by the continued strength of iPhone, Mac and the App Store, which drove our best March quarter results ever,” said chief executive Tim Cook.
Shares in the company rose over 1% after markets closed.
The company which made the biggest profit in corporate history last quarter was not going to beat that in the quieter period after Christmas – but the Apple money machine still goes thundering on, fuelled by the iPhone.
Once again, the company is delighting in beating analysts’ forecasts on just about every count.
The decision to make a much bigger device with the iPhone 6 – an idea which Steve Jobs had rejected – has paid off in spades.
In its conference call with analysts, the company trumpeted in particular the success of the iPhone in emerging markets.
A year ago there were doubts about whether China was ever going to be much of a market for Apple – this last quarter it sold more iPhones in China than in the US.
These results did not include the Apple Watch but Tim Cook enthused about the “overwhelmingly positive” response to the product and said demand was exceeding supply.
But will the watch ever generate the huge mountain of cash that the iPhone has produced? That seems unlikely, and thoughts in Cupertino will already be turning to iPhone 7 as the next product to propel profits to new heights.
There was little information in the figures for investors curious to find out more about the potential boost Apple Watch sales will provide to the firm’s bottom line.
Apple’s newest device – a wearable so-called “smart” watch that encompasses aspects of a fitness tracker and a smartphone – which was available for pre-orders on 10 April, went on sale on 24 April.
Mr Cook said that he was “thrilled” with the initial roll out, but acknowledged that there were some difficulties with providing enough watches to meet customer demand.
“Right now demand is greater than supply [and] we’re working hard to remedy that,” he said.
He also added that unlike with past Apple product launches, understanding how customers engaged with the watch – and what they wanted from the wearable device – was still a work in progress.
“We’re learning quickly about customer preferences – there’s a much larger breadth of possibilities here for customers than our other products,” he said.