Toronto had a 5-on-3 power play for 1:11 starting at 12:26 of the first period but did not score.
"The key to our game tonight was our penalty kill," Winnipeg coach Paul Maurice said. "That was the change in momentum; it got us emotionally engaged in the game. We fed off that and then had the quick strikes right after that."
Tavares cut the lead to 3-2 at 6:47 of the second period when he redirected a pass from Jason Spezza at the top of the crease. Tavares had an assist on Galchenyuk's goal and has scored 10 points (four goals, six assists) in his past seven games.
"I'm just playing, trying to be a difference-maker," Tavares said. "I want to play at a high level consistently and contribute in all areas. I think my focus is always the same, so I'm just trying to build on good habits and do my job out there."
Ehlers made it 4-2 at 5:34 of the third period with his 20th goal of the season. He stole the puck from Mitchell Marner at the blue line, leaving him in alone on Rittich. It was the fifth consecutive season Ehlers scored at least 20 goals.
"I just tried to skate as hard as I could and get my stick on that puck," the forward said. "It created a good bounce for me going towards the net, and I play with a pretty long stick, so that helped out today."
Connor put the Jets up 5-2 with 37 seconds left when he scored into an empty net.
The Jets are 16-8-1 to lead the NHL in road wins.
"To be a good road team, it's a bunch of things," Maurice said. "You've got to be smart, you've got to play hard, you have to be comfortable and patient playing a simple game. The road game is the game that is played in the playoffs, so I would take that."