Nazem Kadri, Jake Gardiner and Kasperi Kapanen scored, and Frederik Andersen made 22 saves for Toronto (8-3-0), which also defeated the Jets 4-2 on Wednesday.
"I thought they played really well tonight, started out hot, but Nazem gave us some energy there but we came back," said Gardiner, who played his 500th NHL game. "You don't see that too often, so it's nice to come back on these guys."
Kadri cut it to 2-1 at 6:33 of the third period, taking a pass from Marner and scoring from low in the right circle. Gardiner tied it 2-2 at 16:49, beating Hellebuyck glove side from the slot.
Kapanen gave the Maple Leafs a 3-2 lead 26 seconds later, getting a loose puck low in the right circle and scoring short side.
"To be honest, I didn't really see anything," Kapanen said. "I just saw the puck kind of come towards me and thought I'd shoot it on net. I didn't see where it went, but am glad that it went in."
Kadri said they were confident they could come from behind despite trailing 2-0 going into the third period.
"We never feel like we're down and out," Kadri said. "They had most of the momentum, but we just needed an early start and a couple of good shifts to start that third period. We scored first (in the third) and that got the ball rolling."
Connor gave Winnipeg a 1-0 lead at 9:38 of the first period on the power play, converting a cross-ice pass from Blake Wheeler at the top of the crease.
Scheifele extended the lead to 2-0 at 11:00 of the second period when he stole the puck from Kadri at the Jets blueline and beat Andersen on the low blocker side on a breakaway.
"It was great, it was right where we wanted it, but we couldn't stop the momentum there during that five or eight-minute span," Wheeler said. "We did a lot of really good things coming off a game last night (2-1 win against Detroit Red Wings), three in four days. It was a pretty good effort, but once they seized momentum, it just seemed like pucks were finding them and they made some good plays."