Paes, playing in his 30th Grand Slam final, had already won the US Open title twice previously with Martin Damm in 2006 and Lukas Dlouhy in 2009.
The fourth seeds took just an hour and 12 minutes to dismantle their higher ranked opponents.
Paes, who has been a runner-up eight times in doubles and won six mixed doubles titles, joins a select few including women's legend Martina Navratilova - with whom he had won two mixed doubles Grand Slams- to have won a Grand Slam title at 40.
I think the best advice I can give to anyone for doubles is get a partner from the Czech Republic," said Paes. "They work hard, and that's what Radek did today. I have to give a big shout out to my partner."
"I never lost the belief that I could come back and (Leander) was always in my corner, waiting for me," said Stepanek, who underwent spinal surgery earlier this year.
The Austrian-Brazilian second seeds were gracious in defeat.
"We had an amazing season...I'm just really happy to reach our first Grand Slam final and I hope to be back again," Soares said during the trophy ceremony.
"We had a great two weeks here, we played some great matches to get to the final. It's no shame to lose to these guys," Peya said.
Appearing tense and nervous in their first Grand Slam men's doubles final, Peya and Soares hit twice as many unforced errors to winners in the opening set.
The Indo-Czech pair, who had ousted top seeds Mike and Bob Bryan in the sems, in no time opened up a 5-0 lead and wrapped up the set 6-1 in just 24 minutes.
Midway through the second set when Paes and Stepanek were up a break at 3-1, Peya took a medical time out. The Austrian had pulled his back muscle in the semis and it came back to haunt him, wiping any chance of a fightback.
He clearly was in discomfort when he returned to court, his first-serve speed dropping down to 70 mph (112 km).
Without taking anything away from the fourth-seeded Paes and Stepanek, it must be said that their opponents, particularly Peya, was in awful touch.
The winners will split USD 460,000 for winning the men's doubles title this year.
--IANS (Posted on 09-09-2013)