Winnipeg moved within three points of the Seattle Kraken, who have two games in hand, for the first wild card.
"We've got six games to go and every single one is a huge one," Jets forward Nikolaj Ehlers said. "So we enjoy this one for tonight and then we move on to the next one."
David Perron and Joe Veleno scored, and Magnus Hellberg made 23 saves for the Red Wings (33-33-9), who defeated the Carolina Hurricanes 3-2 on Thursday.
"I think we had a tough start, but I don't think I showed up to help the team win today," Hellberg said. "I take full responsibility for my performance tonight. It was clearly not good enough. I'm not happy with how I played."
Detroit coach Derek Lalonde did not put all the blame on his goalie.
"As a backup, it's hard. It's a tough position," Lalonde said. "It was just one of those nights he couldn't find the puck and he kept losing his net. I thought he battled through it and it's just tough. There's going to be some of those nights. Obviously we weren't great in front of him, and I just think it kind of piled up on him."
The Jets had been outscored 7-1 in the previous two games and were shut out three times in seven games dating to March 16. Their offense came alive against the Red Wings.
Connor's second goal in 15 games gave the Jets a 1-0 lead when he deflected a Brenden Dillon point shot at 6:56 of the first period.
Blake Wheeler made it 2-0 at 11:57 when Nikolaj Ehlers found him at the edge of the crease for his first goal since Feb. 14, breaking a drought of 21 games.