The win snapped a three-game losing streak.
Matthews converted a Morgan Reilly feed, beating Jets goaltender Connor Hellebuyck high glove side with a backhand shot to give the Leafs the win.
Mitch Marner had a goal and an assist and Frederik Andersen stopped 23 shots as Toronto moved to 19-7-2.
Nikolaj Ehlers scored twice and added an assist and Connor Hellebuyck made 34 saves for Winnipeg who dropped to 16-8-2.
The two clubs finish off their three-game set Saturday night in Toronto.
SHOTS-WINNIPEG 27 TORONTO 38