Neal Pionk intercepted a pass at center ice before moving in and feeding Andrew Copp with a short pass before Copp hit a streaking Appleton with a backhand saucer pass on his way to the net.
Appleton beat Frederik Andersen on his forehand to make it 4-2 Jets.
Winnipeg now stands at 7-0-1 following a loss this season.
Nikolaj Ehlers and Andrew Copp each had a goal and an assist for the Jets.
Josh Morrissey and Kyle Connor also scored for the Jets, who moved to 16-8-1 on the season.
Connor Hellebuyck made 36 saves for Winnipeg.
Auston Matthews had a pair of goals for the Maple Leafs.
Zack Hyman scored the other Toronto goal.
Frederik Andersen turned aside 19 shots for the Maple Leafs, who dropped to 18-7-2.
Zack Hyman gave Toronto the lead 8:16 into the first period after skating nearly the length of the ice before beating Connor Hellebuyck with a backhand.
The goal was his 8th of the season.
Andrew Copp tied it up at 12:20 on the power play.
Auston Matthews scored at 17:44 on the power play, tipping a Morgan Reilly shot past Hellebuyck to make it 2-1 Toronto.
Josh Morrissey tied it 12:45 into the second after moving along the blue line with the puck to find a shooting lane before unleashing a wrister which beat Andersen, clanging off the goal post to score his 1st of the season.
Kyle Connor gave the Jets the lead at 17:42 after Nikolaj Ehlers hustled to a loose puck before setting up shop behind the Toronto net and feeding Connor a Gretzky like pass which Connor promptly buried.
The goal was his 12th of the season.
Mason Appleton scored just under the eight minute mark of the third period before Matthews scored his second of the night with 1:54 remaining in regulation with an extra attacker.
Winnipeg hung on for the win.
The same two teams face each other Thursday night in Toronto.
SHOTS-WINNIPEG 23 TORONTO 39