Paul Stastny gave Winnipeg a 1-0 lead at 18:25 of the first period, getting behind the defense after controlling Dylan DeMelo's saucer pass.
Lewis scored on a wrist shot over Allen's glove to make it 2-0 at 2:20 of the second period. Jansen Harkins got the assist for his first point in 22 games this season.
Suzuki cut it to 2-1 at 4:58 before Lewis made it 3-1 with his second goal of the period at 11:47. Canadiens defenseman Erik Gustafsson overskated the puck after it went to him on a face-off in the offensive zone, and Lewis carried it down the right side on a 2-on-1 with Harkins before scoring with a wrist shot that went in off Allen's left shoulder.
"You get to 3-1 and you're feeling good about your game," Winnipeg coach Paul Maurice said. "And normally there's enough positive feeling on the bench that [if] one bad thing goes on you, you'll be able to hold on. So even coming out into the third, you know at three, you're not dejected by it, they're going a little better. Yeah, that's a tougher one for sure."
Gustafsson replaced Canadiens captain Shea Weber, who was unable to play because of an upper-body injury.
Montreal coach Dominique Ducharme said Weber sustained the injury during a five-game road trip that ended Monday at Calgary. He played 21:48 in a 4-1 loss to the Toronto Maple Leafs on Wednesday.
"It wouldn't be fair to disclose exactly what he's got right now, so we won't do that," Ducharme said. "They're running more tests tomorrow, and hopefully he'll be back soon."
NOTES:Five of Stastny's 13 goals this season have been scored against the Canadiens. … Montreal trailed the Edmonton Oilers by two early in the third period April 5 before rallying for a 3-2 overtime win at home. … The Jets won the season series against the Canadiens 6-3-0.