Toronto (19-6-6) hadn't lost in regulation since Nov. 11. Its streak of 15 straight games with a point (12-0-3) was one short of tying the team record set in the 2003-04 season (14-0-2).
Matt Murray made 17 saves and Michael Bunting scored for Toronto to extend his point streak to 10 games (three goals, nine assists).
The Maple Leafs were 0-for-3 with four shots on goal on the power play.
"That was pretty bad, it was horrible really, not creating a whole lot for our team," Marner said of the power play. "They scored on their power play, we didn't create much off ours. That's something we've got to look at, something we've got to be better at with our mindset, our plays, our passes. We're a lot better than what we showed on that power play."
Chytil put the Rangers up 1-0 with a power-play goal at 3:52 of the first period. He got the puck in the lower part of the left face-off circle and beat Murray high on the far side with a shot that appeared to ricochet off Maple Leafs defenseman Justin Holl.
It was Chytil's first power-play goal since Jan. 2, 2020, and the first of the season for the Rangers' second power-play unit.
Chytil, Kaapo Kakko, Alexis Lafreniere, Vitali Kravtsov and Jacob Trouba came on the ice with a minute remaining in the man-advantage, which is rare because typically the Rangers' top power-play group stays on the ice for at least 90 seconds before changing.
"Finally, we had a little more time and we could make some plays," Chytil said. "We won a face-off, I got good help there on the face-off, and we could make good plays in that 50 seconds that we got there. Finally, we scored."
Rangers coach Gerard Gallant said, "They deserved the opportunity. It was great to see."
Bunting scored off a rebound at 14:06 to make it 1-1. David Kampf deflected Conor Timmins' shot. Shesterkin made the save, but the rebound came to Bunting on the left side and he put it in.
"He's going to the net, doing his thing," Toronto coach Sheldon Keefe said of Bunting. "He's a streaky scorer and he's feeling it right now. He's played well for a good chunk of time so it's good to see him get rewarded."
Vesey put the Rangers back in the lead, 2-1 at 15:33 of the second period, when he got the puck from Trocheck, made a move around a sliding TJ Brodie, went backhand-forehand and roofed a short-side shot past Murray from the right circle.
Vesey said he was thinking short side the entire time, calling it a move he has in his bag from a long time ago.
"I was trying to see what the defenseman's first move was going to be," Vesey said. "I thought he slid a little early so I thought I could get around him. Just used my instincts and lucky enough it went in short-side."