Pierre-Luc Dubois scored, and Connor Hellebuyck made 39 saves for the Jets (31-17-1), who won their previous two games and finished a five-game road trip 2-3-0.
"We played hard for the most part," Winnipeg coach Rick Bowness said. "We just let up when we shouldn't have, and they didn't. Their goalie made some huge saves for them, our goalie made some huge saves for us. It certainly wasn't a 2-1 game in terms of offensive opportunity for either team."
Jets defenseman Josh Morrissey kept it a one-goal game at 18:22 of the third when he blocked a shot by Mikael Granlund from the right face-off circle with the net empty.
Winnipeg then came close to tying it twice in the final minute when Mark Scheifele and Nikolaj Ehlers each hit the crossbar with 44 and 16 seconds remaining, respectively.
"We had our chances, they had theirs," Jets forward Cole Perfetti said. "You know, hit a couple of crossbars late and we created lots, had a lot of great chances. I think, a couple of self-inflicted wounds and things we'd like to clean up. We know we can do better, but I think all four lines worked really hard.
"That was a long road trip. I think the guys are really tired and battled through. I think we deserved a better outcome but, at the same time, their goalie played great. They played a good game. Yeah, it was a good hockey game."