With this win, Paes and Stepanek prevented Bob and Mike Bryan from becoming the most successful men's doubles team in Grand Slam history.
The American duo were bidding for a record-breaking 12th Grand Slam title but defeat means they are still level with Todd Woodbridge and Mark Woodforde's total of 11.
Unseeded Paes and Stepanek headed into the clash as big underdogs against the top seeds but stormed to a shock 7-6 (7/1) 6-2 victory at the Rod Laver Arena.
The triumph means Paes has now completed a career Grand Slam of doubles titles, having never previously won the Australian Open - although this is his first major title with Stepanek.
This was only the duo's fourth Tour-level event together and only Stepanek's second Grand Slam final - his best prior performance being US Open runner-up alongside Jiri Novak in 2002.
On this occasion the Czech tasted glory alongside his Indian partner - but it looked like being a much closer affair during a tight opening set.
After clinching it 7-1 on a tiebreak, Paes and Stepanek then found another gear in the second as they crucially broke the Bryan serve twice to wrap up the win.
The pair's volleying in particular was sensational, and Stepanek said: "We practiced hitting volleys, reflex volleys, every day for the last 21 days."