Michael Frolik scored 1:04 into the third period to give the Jets a 2-1 victory over the Canadiens on Sunday.
Tobias Enstrom also scored for the Jets, and Al Montoya stopped 30 shots.
Brian Gionta scored for Montreal. Carey Price, playing his second game in as many days, made 33 saves.
But the Canadiens felt the Jets should have been called for a penalty as Montreal pressed for the tying goal.
In the final minute, Montreal's Brendan Gallagher was roughed up by three Jets, preventing him from getting out of the offensive zone.
With their net empty, and an extra skater on the ice, Gallagher was kept on the wrong side of the blue line for roughly 20 seconds, so the rest of the Canadiens couldn't enter the Winnipeg zone.
Gallagher was cross-checked into the net by Zach Bogosian, punched and elbowed in the head by Montoya in the crease, and then elbowed again by defenseman Jacob Trouba.
However, no infractions were called.
''There could have been five penalties there,'' said Canadiens coach Michel Therrien, who watched the replay before speaking to the media. ''We're definitely going to ask the league for explanations. It's very frustrating. It could have given us the chance to tie the game.''
But Montoya, who earned his 10th win of the season, wasn't buying any of it. He suggested that Gallagher was doing his best to stay in the zone and draw a penalty.
''No. 11?'' Montoya asked, apparently not knowing Gallagher by name. ''We were all caught up. The referees saw that. They were there. You know he was doing something for a reason.''
After the game, defenseman Josh Gorges spoke to reporters on Gallagher's behalf, calling the 5-foot-9 forward too ''fired up'' and ''heated'' to address questions about the game's final minute.
''I have to be careful with what I say,'' Gorges said. ''It was pretty evident they were not allowing him to get out of the zone. He took a punch to the head from the goalie, got tripped up from the defenseman, and the guy coming off the bench gave him another shot.''
Gallagher was sent to the penalty box three times during the game, for roughing, holding, and tripping. He finished the game with two shots, six penalty minutes and a minus-1 rating.
''I can't comment on how (the referees) feel toward any one individual player,'' Gorges said. ''I don't know if there's a grudge or something. It's too bad.''
Frolik's early third-period goal stood up as the winner. After a Winnipeg dump-in, Price mishandled the puck outside his crease and lost possession to Andrew Ladd. The Jets captain found a streaking Frolik in front of the net, and Price couldn't make it back in time to stop the shot.
The Jets (27-25-5) have won eight of 10 since Paul Maurice took over as coach on Jan. 12. Winnipeg is still last in the Central Division, but the Jets are only four points off the final playoff spot in the Western Conference.
Winnipeg, which has won four of five on the road, beat the Canadiens for the first time in seven meetings.
''We've made some pretty big strides,'' Maurice said. ''There's still a lot to cover. It's what we want our team to look like. We want to define what the Winnipeg Jets' game is. That's going to take a long time to do.
''We're big and we're fast and we're young. We want to use that. We want to be aggressive with our size and our speed.''
Winnipeg came out strong, outshooting the Canadiens 7-0 in the first three minutes. A few key saves by Price kept the game scoreless.
Enstrom put the Jets on the board at 9:13 of the second.
The Winnipeg defenseman carried the puck along the end boards, circled the net and squeezed a shot under Price's glove on the wraparound for his sixth of the season.
After hitting two posts in the period, the Canadiens tied it on a quick release wrister by Gionta at 17:06.
While playing 4-on-4, the Canadiens captain took a pass from Tomas Plekanec on his backhand, quickly switched to the forehand and fired in a sharp shot into the roof of the net.
Despite the no-call at the end, Gorges said the Canadiens shouldn't have waited so long to get even.
''That wasn't the difference,'' Gorges said. ''But it was a frustrating end to the game.''
The Canadiens couldn't benefit from two third-period power plays.
NOTES: Michael Bournival was back in the Canadiens lineup after missing Saturday's game because of the flu. Christian Thomas dressed for the second straight game, and George Parros was a healthy scratch. ... The Jets were without Evander Kane, the team's third-leading goal scorer. He is out with an infection in his hand. ... The Canadiens beat the Jets 3-0 in the teams' first meeting on Oct. 15, 2013.
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