Matthews also had an assist, giving him six points (three goals, three assists) during his four-game point streak.
"Tonight was big one for us against a team that's right up there with us in the standings," Matthews said. "For us, these two games [against Winnipeg] are extremely important."
The teams play again here Friday. Toronto is 3-2-0 against Winnipeg this season and leads the Jets by three points for first place in the Scotia North Division.
Zach Hyman had a goal and an assist, and Mitchell Marner had two assists for the Maple Leafs (23-10-3), who are 4-0-1 in their past five games. Jack Campbell made 26 saves and is 7-0-0 this season.
Josh Morrissey scored, and Connor Hellebuyck made 23 saves for the Jets (22-13-2).
"Unfortunately we had some penalties, which kind of takes the flow out of the game in a game where you're trying to get your legs under you early," Morrissey said. "We really weren't able to. I really liked our game after that. In the second period we had a lot of great chances, we were all over them. They played a pretty solid game after that, didn't give us a lot. I guess you could say they scored a few in the first and we only scored one in the game, so we lost the first period and we ended up losing the game."
Matthews gave the Maple Leafs a 1-0 lead at 4:40 of the first period.
Hyman scored to make it 2-0 at 10:47. The goal was upheld after the Jets challenged for goalie interference.
"The start was huge, going up 2-0 early, it's a lot easier to play when you got the lead than when you're coming from behind," Maple Leafs forward Alex Kerfoot said. "So that was big. I just though that we played a bit more of a complete game and [Campbell] did a great job back there shutting the door."
Kerfoot scored shorthanded on a breakaway to make it 3-0 at 16:40 of the second period.
"A huge goal for us. A big moment in the game," Maple Leafs coach Sheldon Keefe said. "Obviously we don't like giving the one back right after that … [the Jets] get the one you kind of expected they might within the number of minutes we gave them on the power play. It's not [a big] deal because we get that shorty."