The 7-6 (7/1), 6-2 victory was the first for India's Paes over American twins Bob and Mike Bryan in a final after five defeats in title matches, and means he completes a career Grand Slam of doubles titles.
Coming into the Australian Open the Indian doubles specialist had won 47 career doubles titles with 11 different partners, including one with Stepanek, who now claims his first Grand Slam doubles title.
"I know what this means for him (Paes) because this title was missing from his career Grand Slam, and I'm happy I can be by his side," Stepanek said.
The two danced around the court gleefully after their win, which comes on the day that Bob Bryan's wife is expecting their first baby.
"She's probably going to deliver tomorrow so thanks baby, thanks for holding it in for me," he said.
Serve dominated in the first set with just a single break point for each pairing and no breaks of serve, but unseeded Paes and Stepanek stepped up their game in the tie-break to take it 7-1.
The fired-up Indian-Czech pairing finally broke the Bryans' serve in the second game of the second set and looked like they would run away with the match.
The Americans, with 76 titles together, stopped the rot by holding in the fourth game but they could not reverse the momentum and were broken again to slip to a comprehensive defeat.
Paes and Stepanek, playing in just their fourth Tour-level event together, had lost to the Bryan brothers in straight sets in both their previous meetings.
The result means the Bryans remain on 11 titles, sharing the record for the number of men's titles in the open era with Australia's Todd Woodbridge and Mark Woodforde.