Connor scored again to make it 3-2 at 11:50 before Blake Wheeler tied it 3-3 at 14:31.
"You look at that second period, they started stressing us out," Canadiens forward Jonathan Drouin said. "We were giving them too much space in the neutral zone for them to skate and make plays and they kind of took us apart. They have skilled players. You look at that top six, it's probably one of the best top sixes in the League."
Nate Thompson gave Winnipeg a 4-3 lead at 6:37 of the third period. It was his first goal in his seventh game with the Jets, who signed the 36-year-old forward as a free agent Oct. 10. He played for the Canadiens from 2018-20.
"That's the biggest reaction on the bench, is when a guy like [Thompson] scores and it's his old team and it ends up being the game-winner and you've clawed your way back," Jets coach Paul Maurice said. "When you block shots for a living and when your lot in life is that you've got to do the hard and heavy things, it's good not just to score, but to score the big goal."
Dubois scored at 12:37 to make it 5-3, and Scheifele scored into an empty net at 18:22 for the 6-3 final.
NOTES: Scheifele has 17 points (seven goals, 10 assists) on an NHL career-high 11-game point streak. … Canadiens forward Josh Anderson left after playing 4:24 in the first period. Ducharme did not have a postgame update. … Armia had his second two-goal game of the season. His first was Jan. 21 against the Vancouver Canucks when he had two goals and two assists in a 7-3 win. … Wheeler had two assists for five in his past two games.