Tatar's second-period goal started the Red Wings on their way to erasing a 2-0 Winnipeg lead. He scored the game-winning goal with 4:50 left when he buried a shot past Winnipeg goaltender Ondrej Pavelec.
Tatar has a four-game point streak (four goals, one assist). The 23-year-old left wing has seven goals in his past 10 games after starting the season with one goal in his first nine. Johan Franzen and Justin Abdelkader scored for the Red Wings.
"It's great to see [Tatar] getting two [goals]," Franzen said. "He is one of those guys, he grows when he scores. He loves it, so it's good to see."
"He's a good goalie," Red Wings coach Mike Babcock said of Mrazek. "He's totally relaxed and just thinks that he is going to win."
Pavelec made 23 saves. It was his first start since being pulled after allowing three first-period goals in a 4-3 shootout loss at the Minnesota Wild on Sunday.
"We lost against a really good team," Pavelec said. "Overall I think the game was OK. We just couldn't finish it in the third period. The third period, we should play a little smarter. But we played hard."
Detroit played without center Pavel Datsyuk (groin) and defenseman Brendan Smith (hand), as it continued its three-game road trip. The Red Wings play the Toronto Maple Leafs at Air Canada Centre on Saturday.
The Red Wings have wins in three of their past four games but struggled in the first two periods Thursday and produced 13 shots. They sent 14 shots at Pavelec in the third period.
"We were standing around watching them and didn't want to get involved in the game," Babcock said. "Our goaltending was good and our penalty kill was good. They kept us in the game. We got upset, or whatever we did, we finally dug in and got playing. Once we got executing, we had lots of opportunities around their net. In the end, it's a big road win for us.
"It's hard to shoot [the puck] when you don't have it. I just thought that we gutted it out. We had good leadership in our [dressing] room. We had leadership on the bench. We just dug in and found a way to get it done.
"I like the team. I think we have a chance to be a good team. I keep telling the guys that. Just like most teams in the [NHL], we're a work in progress and trying to get better."
Byfuglien broke a 14-game goalless streak 2:15 into the second period. Evander Kane worked the puck to the edge of Mrazek's crease, where Byfuglien flicked the bouncing puck over the goaltender's left shoulder. Byfuglien's third goal was his first since Oct. 21.
Lowry broke his 14-game goalless streak at 9:32 with his second goal of the season. As part of a recently assembled line with center Mark Scheifele and right wing Michael Frolik, Lowry broke loose from the Detroit defense in front of Mrazek and poked a bouncing puck into the net.
Detroit moved back to within a goal 30 seconds later. Tatar skated into the right circle and scored his seventh of the season on a low shot past Pavelec.
Detroit used its power play to tie the game 2-2. Franzen skated around Winnipeg defenseman Mark Stuart before beating Pavelec with his sixth goal of the season. Franzen has four goals in his past six games.
Perreault's wrist shot from the bottom of the left circle put the Jets ahead by a goal with 3:48 left in the second period. He went without a goal in his first 19 games this season before scoring Tuesday against the New Jersey Devils.
The Red Wings' third-period push began with a chat inside the Detroit dressing room.
"We were down 3-2, but we were saying after the second period that we have to go hard to the net and get some rebounds and some greasy goals," Mrazek said.
Tatar credited the push to an adjustment the Red Wings made breaking out of their defensive zone.
"We said after the second period that we have to exit the zone really fast and way [more easily] than we're used to, because [Winnipeg was] very heavy and they forecheck well," Tatar said.
Abdelkader's sixth goal of the season tied the game 3-3 when he jabbed a rebound under Pavelec with seven minutes left.
The Jets finished a stretch of nine of 11 games on the road. They continue their homestand against the St. Louis Blues on Sunday.
"[Detroit is] going to make a push down a goal," coach Paul Maurice said. "To be honest with you, I think it was 15 games in  days, twice off the East Coast. The bench didn't get quiet out or anything, but they were breathing pretty [heavily]. We just didn't have the fight on some pucks."
Tatar will turn 24 on Dec. 1 and is in his second full season with the Red Wings. Last season Tatar, a second-round pick in the 2009 NHL Draft, scored 18 goals. Babcock said he will continue to push Tatar and did not think he had played well before the Detroit comeback.
"[Tatar] is a competitive kid," Babcock said. "I might be harder on [Tatar] than anybody [else] on the team, just because I think [he] has a chance to be a real player, and we're going to hold him to that.
"We think he should be good every night, because he is capable of being good every night and every shift. So we expect a lot from [Tatar], and he is capable of delivering."