Mark Scheifele and Andrew Copp each had a goal and an assist for the Jets (27-16-3), who lost a second straight in regulation for the second time this season. Laurent Brossoit made 25 saves in relief of Connor Hellebuyck, who allowed three goals on six shots in through 11:59 of the first period.
"Definitely not the start we wanted, but we kept on clawing back and tried to get some chances," Scheifele said. "We fought right to the end and made it a close one. It would have been nice to get that one into overtime."
Toronto extended its lead to six points over second-place Winnipeg in the seven-team Scotia North Division having played one more game. They play again here Saturday.
"We needed to get a win here today. No matter who we were playing we needed to get back on the right side of it," Maple Leafs coach Sheldon Keefe said. "We had to turn the light bulbs on there for the third period and make sure we took care of this one.
"In terms of the standings and everything like that, we didn't talk about that a great deal. I think no matter who were playing today we knew we needed a good effort and I think that we did that here today, but a lot of things we could do better, and we're certainly going to have to do that on Saturday."
Matthews scored his NHL-leading 34th goal 27 seconds into the first period, and Wayne Simmonds scored at 1:18 to give the Maple Leafs a 2-0 lead.
Scheifele cut it to 2-1 at 3:19, and Copp tied it 2-2 at 10:26.
"It's 2-2. They didn't run all over us," Jets coach Paul Maurice said. "Certainly we weren't better than they were, but I don't know how much better they were than us. It was 2-2 early enough in that game."