Apple reported a net profit of $18bn (£11.8bn) in its fiscal first quarter, which tops the $15.9bn made by ExxonMobil in the second quarter of 2012, according to Standard and Poor’s.
Record sales of iPhones were behind the surge in profits.
Apple sold 74.5 million iPhones in the three months to 27 December - well ahead of most analysts’ expectations.
In a conference call with financial analysts Apple’s chief executive Tim Cook said that demand for phones was "staggering".
However, sales of the iPad continued to disappoint, falling by 18% in 2014 from a year earlier.
The demand for Apple’s larger iPhone 6 Plus model appeared to help boost profits and increase the iPhone’s gross profit margin - or how much Apple makes per phone - by 2% to 39.9%.
However, Apple did not give a breakdown of sales for the iPhone 6 and other models.
Apple shares rose more than 5% in trading after the US markets had closed.
Buster Hein, who edits the "Cult of Mac" website, told the BBC that iPhone sales had surpassed expectations.
"Oh my gosh, it’s unbelievable," he said. "I mean, a lot of us were expecting good iPhone sales during the holidays, but I don’t think anybody really thought Apple was going to blow past 70 million units sold," he said.
"Apple became the number one smartphone company in China in the last quarter, which was just huge for them," he added.
Apple’s revenue grew to $74.6bn in 2014 - a 30% increase from a year earlier.
However, on a conference call to discuss earnings, Mr Cook complained of "fierce foreign exchange volatility", which added Apple to a growing list of US firms who have been hurt by the strong dollar abroad.
Apple said that currency fluctuations shaved 4% from its first-quarter revenue.
Sales in greater China hit $16bn in 2014 - a 70% increase from a year earlier, and almost equalling the $17bn in sales the company recorded in Europe last year.
A report by research firm Canalys released on Tuesday said that Apple had overtaken competitors to become China’s number one seller of smartphones by units shipped in the fourth quarter of 2014. Apple also said that its newest product, the Apple Watch, was still on schedule and would begin shipping in April. - BBC