But the Frenchman refused to bow out quietly. They saved four match points to level at 9-9.
A Bryan forehand volley gave the Americans a fifth championship point. But that was squandered when Sock’s forehand drive went wide.
Herbert and Mahut then had a chance to take the title at 11-10 up but Bryan saved that with an overhead smash at the net. The 40-year-old then set up his team’s sixth match point with a service winner.
The crown was collected when Herbert served a double fault - the pair's 10th - after a shootout lasting 16 minutes.
It was a damp way to end such an enthralling contest especially after the French duo had taken the early advantage in the match.
They edged the first set 7-5 after 48 minutes but they soon found themselves a break down in the second set.
“It went too quickly for us,” Mahut reflected after the match. “We were behind so fast in the second set and we never recovered.”
Bryan and Sock claimed the second set 6-1 in 24 minutes and took that vitality into the match tiebreak.
“They started creeping back,” said Bryan of the French pair’s return from the abyss. “They won one point on my serve, one on Jack's serve. All of a sudden we're down match point. That's the way it goes.
“You need a little bit of luck to win these matches.So I feel lucky. I think we saved the best for last because you have to in order to beat that team. They don't back down.”
The ATP Finals trophy was Bryan and Sock’s third big title of the year. The pair came together after Bob Bryan – Mike’s usual partner – withdrew from the tour with an injury and they have won Wimbledon and the US Open. Bob Bryan is back in training and will resume his partnership with his twin brother for the start of the 2019 season.
“I think Bob is itching to get back on tour,” said Bryan. “He was watching us on TV. He wants another taste of the competition, the top level of doubles.
“If he does, then I'll be his guy. I think we want to go out together. We came into this world together and we'll definitely end our careers together.”