The win snapped a three-game losing streak for the Maple Leafs.
William Nylander had a goal and an assist for Toronto.
Matthew Knies and Morgan Reilly also scored for the Maple Leafs.
Max Pacioretty had three assists for Toronto.
Anthony Stolarz turned aside 19 shots for Maple Leafs, who moved to 5-4-1.
Kyle Connor scored three goals for Winnipeg.
Mark Scheifele scored the other Jet goal.
Josh Morrissey had three assists.
Connor Hellebuyck made 30 saves for Winnipeg, who lost their first game of the NHL season to drop to 8-1-0.
Tavares opened the scoring just under the twelve minute mark when he shoveled a Max Pacioretty cross crease feed past Hellebuyck to score his third of the season.
William Nylander gave the Leafs a two-goal cushion at 17:47 after he snapped a shot past Hellebuyck following a Neal Pionk turnover along the end boards.
Pacioretty got to the loose puck at the bottom of the faceoff circle and slid the disc to Nylander, who made no mistake, snapping the disc past Hellebuyck high blocker side.
Matthew Knies made it 3-0 56 seconds into the second stanza after he scored on a rebound off an Auston Matthews shot.
Morgan Rielly scored at 3:25 with a hard wrister, beating Hellebuyck just inside the right post.
The goal was his 4th of the season.
Kyle Connor got Winnipeg on the board with a power play marker at 6:19 of the second after converting a Mark Scheifele cross ice feed, beating Stolarz high glove side.
Connor fired his second power play marker of the night at 11:25 when he snapped a Josh Morrissey feed past a screened Stolarz to cut the Toronto lead to 4-2.
Jets Head Coach Scott Arniel had a blunt assessment of his club's effort on the night.
"It was throughout. Whether it was our ready to go, ready to compete, ready to get into it, I don't have an answer for you. Toronto was a heck of a lot better than we were. They wanted it. They came in here and gave us a punch right in the nose in the first two periods. It was a little late when we responded, but it's not good enough. We didn't come out the way we wanted to come out."
"It just felt like everybody was off. Everybody was, like you said there was momentum building. Then all of a sudden there was a mistake or a turnover or bad coverage, whatever, and all of a sudden Toronto's getting great chances. The first two periods, that was a lot of what we did. It was just, we kind of shot ourselves in the foot," said Arniel.
Tavares counted his second of the night at 17:33 of the second period when he popped a backhand shot past Hellebuyck to make it 5-2 Toronto.
The goal was his 4th of the season.
Mark Scheifele scored 7:46 into the third, one timing a Kyle Connor feed just under the cross bar to make it 5-3.
Kyle Connor got his third of the game at 16:13, ripping a shot past Stolarz through a screen to make it 5-4.
The goal was his 9th of the season.
The Jet winger said there was no quit by his team.
“Well, we got it down to one, and we were pressuring there. There’s no quit in this room. We wanted to come out and push and show some good work ethic there in the third and see what happens," he said.
John Tavares added an empty netter to seal the win for the Maple Leafs at 19:35 of the third.
Maple Leafs Head Coach Craig Berube liked his club came out.
“That’s exactly what we needed, for sure, especially coming into this building. It’s a tough building and a very good team we’re playing tonight. I liked our mindset right away in the game of playing fast and quick and north, good forechecks. We got pucks to the net that we hounded after. We were just on top of things.”
SHOTS-TORONTO 36 WINNIPEG 23
ATTENDANCE-14,325
