"You could see we didn't have a lot of confidence in the third, but we stayed with it and battled," Red Wings coach Jeff Blashill said. "We got it to overtime and ended up winning it."
Larkin gave the Red Wings a 1-0 lead at 6:08 of the second period, beating Mrazek with a wrist shot from the right face-off dot.
"It felt pretty good to score on Petr," Larkin said. "I was getting worried in the first period, because he looked so comfortable out there."
Luke Glendening made it 2-0 with a shorthanded goal at 7:59, beating Mrazek to the short side with a wrist shot over his glove from the right face-off circle.
"I played that all wrong," Mrazek said. "I know he will shoot from anywhere when he's killing, so he didn't surprise me. I just didn't get it."
Sean Couturier scored his 30th goal, on the power play, at 8:53 to make it 2-1 after Claude Giroux hit the post.
Evgeny Svechnikov scored his first NHL goal at 9:57 to make it 3-1 and chase Mrazek.
"I got a great bounce," he said. "I tried to feed [Martin] Frk and they blocked it, and it bounced right on my tape. I shot it and it went in. That was the best feeling."