Later in the period, with Jeff Petry in the box, Rem Pitlick broke away and was awarded a penalty shot after Pierre-Luc Dubois slashed him, but Pitlick couldn't capitalize.
The Jets retook the lead moments later, when Andrew Copp scored his 13th of the season.
After 40 minutes, Montreal trailed 5-4 and was outshot 11-10 by Winnipeg in the second.
In the third, with Brendan Gallagher in the box, Scheifele gave the Jets a two-goal cushion with his second of the night at the 2:46 mark.
Dubois made it a 7-4 game with another power play goal just over three minutes later.
Andrew Hammond replaced Sam Montembeault in goal following the Dubois tally.
Paul Stastny added an eighth goal with 2:34 remaining in the game.
The Canadiens' next game takes place Thursday night against the Flames in Calgary.