Apple's revenues hit 57.6 billion US dollars for the last three months of 2013, a new quarterly record for the company.
Profits of 13.1 billion dollars were also made - equal with the record profits set 12 months previously.
Apple sold 51 million iPhones - a new high for the company, though short of forecasts peaking at 60m - 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 (54.5 billion dollars), to subsequent figures of 43.6 billion dollars, 35.3 billion dollars and 37.5 billion dollars.
Last quarter, Apple sold a record-breaking 33.8 million iPhones but experienced a drop in sales of Mac computers.
Peter Oppenheimer, chief financial officer, said: "We generated 22.7 billion dollars in cash flow from operations and returned an additional 7.7 billion dollars in cash to shareholders through dividends and share repurchases during the December quarter, bringing cumulative payments under our capital return programme to over 43 billion dollars."
Apple expert Professor Loizos Heracleous from the Warwick Business School said the figures showed the technology superpower had sustained reasonable growth.
But he identified areas of concern for the business and shareholders. "Even though Apple has achieved record revenues and profits, the growth rates of its leading products (iPhone, iPad) are reducing. This means that to recapture the rates of growth that Apple historically delivered, there should be new product introductions of the calibre of these leading products," he said.