It equalled its first quarter profits of $13.1bn (£7.9bn) for the final quarter of 2012.
The results reversed a profits slump and post record revenue figures.
It was the first period fully taking into account sales of the iPhone 5s and iPhone 5c, as well as marking the launch of the iPad Air and iPad mini.
Apple sold 51 million iPhones - a new high for the company - while iPad sales also set a new record of 26 million.
The company also sold 4.8 million Macs, compared with 4.1 million in the year-ago quarter.
Tim Cook, Apple chief executive, said: "We are really happy with our record iPhone and iPad sales, the strong performance of our Mac products and the continued growth of iTunes, software and services.
"We love having the most satisfied, loyal and engaged customers, and are continuing to invest heavily in our future to make their experiences with our products and services even better."
The figures reverse a slump in revenue - from the all-time high a year earlier ($54.5bn), to subsequent figures of $43.6bn, $35.3bn and $37.5bn.
Last quarter, Apple sold a record 33.8 million iPhones but experienced a drop in sales of Mac computers.
Peter Oppenheimer, chief financial officer, said: "We generated $22.7bn in cash flow from operations and returned an additional $7.7bn in cash to shareholders through dividends and share repurchases during the December quarter, bringing cumulative payments under our capital return programme to over $43bn."