Apple has smashed into the record books by reporting the largest quarterly profit in corporate history.

The tech company – already the most valuable on the stock market – reported profits of $18bn (£11.9bn) for the third quarter of the fiscal year, surpassing the previous record quarters set by oil companies ExxonMobil and Gazprom.

Apple chief executive Tim Cook called the company’s sales “phenomenal” and said the company had sold 34,000 iPhones an hour every day of the quarter. “This volume is hard to comprehend,” Cook said.

A record 74.4m iPhones were sold in the three months to the end of 2014, the California-based company announced on Tuesday, comfortably beating analysts’ expectations as sales of its two newest models soared during the Christmas holidays and found new fans in China.

The record $74.6bn in revenues for the all-important third quarter was well ahead of the $67.5bn expected by analysts. Apple, the world’s most valuable company, ended the quarter with $178bn in cash.

Sales were led by China, up 70% on a year ago. Sales in the Americas and Europe were up 23% and 20% respectively.

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The iPad’s popularity continued to wane, however. Apple sold 21.4m of the devices in the last quarter of 2014, less than analysts had expected, but iPhone sales cheered investors. Ahead of Apple’s announcement, analysts had predicted the company would report sales of iPhone 6 and iPhone 6 Plus of between 66m and 70m over the quarter. Apple’s shares jumped 5% in after-hours trading on Tuesday.

“We’d like to thank our customers for an incredible quarter, which saw demand for Apple products soar to an all-time high,” said Cook. “Our revenue grew 30% over last year to $74.6bn, and the execution by our teams to achieve these results was simply phenomenal.”

Apple had a record-setting year in 2014, with its share price hitting new highs and taking its stock market valuation to $650bn. Last week, the company revealed that Cook’s pay package more than doubled last year, to $9.22m. Angela Ahrendts, Apple’s new head of retail, took home the biggest award in 2014 – $73.3m – boosted by a massive sign-on package.

The performance beat Apple’s previous quarterly record for iPhone sales, 51m, set in the quarter ending 28 December 2013.

Apple’s latest iPhones were introduced in September and have proved a hit with consumers. The company had eschewed making iPhones with larger screens until last year, and the decision to take on rival Samsung and others with a larger smartphone appears to have paid off.

The introduction of the larger iPhone 6 Plus alongside the iPhone 6 and lower-priced iPhone 5S and 5C pushed Apple’s iPhone sales past 20m a month for the first time in November, according to recent research from Counter Point. Japan, Korea and China have proven bright spots for Apple, with higher-than-expected demand for the iPhone 6 and iPhone 6 Plus models.

Apple also managed to increase the amount of money it charges for iPhones over the quarter. The average selling price of the iPhone was $687 in the final quarter of 2014, compared with $637 for the same period a year ago. The iPhone 6 Plus costs $100 more than Apple’s previous high-end model.

In the US, iPhone owners accounted for 42.3% of all smartphone users in 2014, according to eMarketer, up from 40% in 2013. By comparison, Android users accounted for 51.3% in 2014, up from 50.5% the previous year.

According to eMarketer, there were 76.2m iPad users in the US in 2014, or 51.8% of all US tablet users. That market share was down from 54.5% of all US tablet users in 2013.

In the UK, the number of iPad users reached 15.7m in 2014, up from 12.9m in 2013, eMarketer estimates, but Apple lost market share, falling to 53% of tablet owners from 57% in 2013.

Apple is preparing to launch the Apple Watch, its first truly new product line under Cook, who took over following the death of co-founder Steve Jobs in 2011. The smartwatch is expected to go on sale in April. Cook said his expectations for the watch were “very high”.

“I’m using it every day, love it, can’t live without it,” he said of the watch.

The product launch comes as Apple is struggling to sell iPads in the face of cheaper alternatives, winding down sales of its iPod media players and increasingly concentrating on services like Apple Pay, its credit card-less payment system that can be used with iPhones and the new watch.

Cook said that some 750 banks and credit unions have signed on for Apple Pay and that the service already comprises more than two-thirds of all contactless payments. He said Whole Foods had reported a 400% rise in contactless payments thanks to Apple Pay.