WINNIPEG, Manitoba -- Tomas Tatar followed his coach's advice, and was rewarded with a two-goal game.
Red Wings coach Mike Babcock had told his players to keep shooting the puck at the net after the team lost 4-1 to Montreal on Sunday.
"I guess (Babcock's) right. He's been in the league forever," said Tatar, who had three shots. "He's a great coach.
"We want to score always, but sometimes it doesn't go our way, so you have to play simple and just put the puck on the net. We were more aggressive. We knew we had nothing to lose, so we just wanted to force the puck to the net."
Detroit rested Jimmy Howard after he was in net for the Red Wings' 5-0 victory over Columbus on Tuesday. With backup Jonas Gustavsson out because of a dislocated shoulder, Petr Mrazek played in his 12th career game -- and first this season -- and made 28 saves.
Detroit was without center Pavel Datsyuk (groin) for a second straight game.
Even though the Red Wings trailed 3-2 after two periods, they outshot the Jets 14-9 in the third.
Tatar scored the winning goal at 15:10 of the third period when he one-timed a pass from Abdelkader.
Abdelkader had tied it 3-3 with seven minutes left after he appeared to tip in Brian Lashoff's long shot that Pavelec might have pushed in.
The Jets built a 2-0 lead after a scoreless first period.
Byfuglien ended his 14-game goal drought off a nifty setup by Evander Kane. Kane was at the side of the net and sent a between-the-legs backhand pass that Byfuglien used to score his third of the season at 2:15 of the second.
"We worked the first 40 (minutes) pretty good as a team," Byfuglien said. "There were a few little things that we could have done better.
"Throughout the whole year we've stuck together and played pretty good as a team. You're going to have your games where you get a few mistakes and it ends up in the back of the net."
Rookie Adam Lowry scored his second goal off a rebound at 9:32.
The Red Wings didn't get their first shot in the second period until almost 11 minutes in, but they quickly made up for it.
Just 30 seconds after Lowry's goal, Tatar took advantage of defenseman Toby Enstrom's turnover, intercepting his pass and beating Pavelec with a high shot to make it 2-1.
Then, with Enstrom in the penalty box for tripping, Franzen scored his sixth when he went around falling defenseman Mark Stuart and scored the tying goal at 12:52.
"Our goaltender was good and our penalty kill was good, and that kept us in the game," Babcock said. "Then we got upset or whatever we did, but we finally dug in and got playing. Once we got executing, we had plenty of opportunities around their net.
"In the end, it's a big road win for us."
Perrault, who assisted on Byfuglien's goal, put the Jets ahead 3-2 with just under four minutes left in the second.
Perrault took a pass from Jacob Trouba around Winnipeg's blue line and skated down the boards. He took a shot, got his rebound, went behind the net, and then spun around at the side and beat Mrazek at 16:12.
Winnipeg, which beat New Jersey on Tuesday, will finish a three-game homestand Sunday against St. Louis. ... Detroit will travels to Toronto for a game on Saturday.