The Jets rank third in the North Division, four points up on the fourth-place Canadiens, who hold the final playoff spot. Calgary is six points behind Montreal.
Winnipeg won the season series with Montreal 6-3, including three overtime victories, but losing the finale allowed the Canadiens to gain ground.
The Canadiens trailed and chased for two periods before tying it up 3-3 late in the second. With Montreal on the power play, Armia got his stick on the puck in the slot to beat Hellebuyck between the pads with 1:46 left in the period.
Suzuki got the tiebreaking goal on the power play with 4:50 left in the third, getting his 12th of the season on a rising wrist shot.
Toffoli’s empty-netter with 1:23 remaining sealed the win.
Stastny gave the Jets a 1-0 lead with 1:35 left in the first period. Dylan DeMelo sent the puck to Stastny slashing through the middle to score with a wrist shot for his 13th.
Winnipeg doubled the lead 2:20 into the second, when Harkins threaded the puck through the defense for Lewis to score on Allen far side. It was his fourth.
Suzuki got the Canadiens on the scoreboard at 4:58 as he got a loose puck in the slot and beat Helleybuyck with a low shot glove side.
Lewis got his second of the night at 11:47 on an odd-man rush with Jensen Harkins. Lewis went end-to-end with the puck after Montreal’s Erik Gustaffson overskated it and scored his fifth.
The Jets got caught on a line change and Montreal had all kinds of time for Lehkonen to finish a passing play at 13:44 to make it 3-2.
Canadiens defenseman Jeff Petry extended his assist streak to three assists in three games.
Forward Adam Lowry (upper body) missed a fourth straight game, but coach Paul Maurice said he might be able to return to full practice Sunday. Winnipeg forward Nikolaj Ehlers is out for the rest of the regular season with an upper-body injury.
Montreal captain Shea Weber was a game-time scratch with a lower-body injury. The defenseman joined a number of key Montreal players sidelined. Goaltender Carey Price (concussion) and forwards Brendan Gallagher (broken thumb), Jonathan Drouin (leave of absence), Paul Byron and Tomas Tatar (lower body) remained out of the lineup with each missing multiple games.