While iPhone sales went up iPad sales slumped to 13.28 million iPad units, down 9.2% from 14.6 million units in the same period a year earlier.
Sales of Mac computers, meanwhile, rose 17.6% to 4.4 million units from 3.8 million units last year.
Next month Apple will release their iPhone 6 and a major refresh of the company's flagship product range.
In the same quarter 2013 Apple sold 31.2M iPhones with an average gross margin of 39.4%.
"We're thrilled with the results, and we're thrilled with where we are going. The momentum is really strong," Apple Chief Executive Tim Cook said in an interview with The Wall Street Journal.
Key to Apples increased revenue was increased sales of iPhones from Brazil, Russia, India, and China.-collectively known as the BRIC countries.
"The BRIC countries were unbelievable," said Mr. Cook, noting that iPhone sales in those countries rose 55%, including a 48% increase in China alone.
The WSJ said that in the past few years, the June quarter has been the slowest for Apple as the company gears up with new products ahead of the year-end. The technology giant is banking on an expected new product push of larger iPhones and a series of smart watches before year-end to reinvigorate earnings that have flattened after more than a decade of remarkable growth, raising concerns that Apple is losing its innovative touch.
Apple said profit in its fiscal third quarter was $7.75 billion, up 12.3% from $6.9 billion in the year-ago period.
Revenue rose 6% to $37.43 billion from $35.32 billion in the same period a year earlier.
Apple shares were relatively flat in after-hours trading.
For the current quarter to September, Apple is forecasting a wide revenue range of $37 billion to $40 billion, below analysts' consensus projections of $40.44 billion.
When arch rival Samsung reports earnings next week, the Korean Company is expected to report a third straight year-over-year decline in quarterly operating profit, hurt by price competition and a supply glut of smartphones.