India's Paes and Czech Stepanek, playing in their fourth tour event, broke the Bryans early in the second set and cruised to victory in front of a small but vocal crowd at Rod Laver Arena.
Paes beat the Bryans for the first time in a final after five straight losses, including three at Melbourne Park, and completed a career grand slam of men's doubles titles.
"I know what this tournament means for him, because only this title was missing in his career grand slam," his partner Stepanek said at the presentation ceremony.
"And I am happy and honoured to play by your side."
The Bryan brothers remain level with Australian doubles greats Mark Woodforde and Todd Woodbridge's 11 grand slam titles.
Bob Bryan played out the final on the same day his wife Michelle was due to give birth to their first child.
He said the moment had not yet arrived and hoped to rush back in time to be by her side.
"Thanks baby, thanks for holding it in for me!" he said to chuckles from the crowd.