But the Maple Leafs, who were playing the second of a back to back after losing 4-3 in overtime at the New York Islanders on Monday, responded early in the third.
Shesterkin stopped Marner on a 2-on-1 and Jacob Trouba made a sliding block on Tyler Bertuzzi's shot off the rebound, but Erik Gustafsson interfered with Marner on the play, giving the Maple Leafs a power play at 1:22.
Marner gave Toronto a 5-3 lead seven seconds in at 1:29 on a high tip of Morgan Rielly's shot from the point.
"We only had one [power play] in the first but 'Mo' and I were talking, just try to be open for a high tip there," Marner said. "We knew it was possibly there. Then in the third you see us talking and we said, 'Let's try to look for that again.' Lucky enough I was able to find a quiet spot. 'Mo' with a great shot, I got a piece of it and lucky enough it went in."
The Maple Leafs rolled from there, limiting the Rangers chances to get back into the game before Matthews made it 6-3 at 17:11 with his second goal of the game. David Kampf scored an empty-net goal at 18:33 for the 7-3 final.
"It felt like we were a tired team a lot of the night quite honestly, I didn't think we had our legs," Toronto coach Sheldon Keefe said. "But we were just encouraging and pushing our guys to dig in, move their feet, close and pressure the puck. If we weren't going to get our chances from that at the very least, we were going to pin them down and keep them far away from our end.
“And then through that we drew some opportunities, had some chances at the net, drew a penalty, which really changed the game with our ability to score as quickly as we did on that power play."