Kessel picked an opportune time to score his first goals in 10 games as Toronto (22-13-4) remained fifth in the Eastern Conference standings. More importantly, the Leafs moved four points ahead of idle Ottawa with their fifth win in six games.
The victory was also sweet redemption for Toronto, which couldn't hold a 2-0 lead against New York at the Air Canada Centre on Jan. 26 en route to dropping a 5-2 decision.
And they did it in dramatic fashion as Derek Stepan pulled New York into a 3-3 tie at 9:00 of the third period, converting a 2-on-1 break for his 14th of the season just as a Leafs' power play expired. But Kessel put Toronto back ahead just 39 seconds later with his 12th of the season.
The Rangers (19-16-4) remain tied with the idle New York Islanders for seventh in the Eastern Conference with 42 points.
Toronto visits New York on Wednesday night in the final regular-season meeting between the two teams as the Leafs chase their first playoff berth since 2003-'04.
Rick Nash had the other two goals for New York, which fell to 7-10-2 on the road this season.
Van Riemsdyk had the lone goal of an overly cautious first — Toronto outshot New York 8-7 but the Rangers put two shots off the post. Henrik Lundqvist made the initial save off an open van Riemsdyk in front before the Leafs forward banged the rebound in at 11:04 for his 16th of the season.
O'Byrne, obtained at the trade deadline, put Toronto ahead 2-0 at 11:28 of the second, taking a nice setup pass from Nazem Kadri and firing a shot past Lundqvist. It was his second goal of the season and first with the Leafs.
Nash cut Toronto's lead to 2-1 at 14:55, driving to the Leafs' net and recording his 16th of the season. But the Leafs regained their two-goal advantage on Kessel's power-play goal at 19:18, his 11th. Kessel's wrist shot eluded Lundqvist with van Riemsdyk parked in front.
Nash made it a one-goal game again at 2:50 of the third, skating in from the corner around the Toronto defence and in front of James Reimer before beating the Leafs' goalie with a wrist shot at 2:50.
NOTES — Lundqvist had allowed two or less goals in 10 consecutive starts prior to Monday's game . . . Toronto forward Joffrey Lupul missed his second straight game with an upper-body injury sustained Thursday against Philadelphia. Lupul had been the Leafs' hottest player prior to his injury, registering eight goals and six assists during a seven-game points streak . . . The Leafs wore their third jersey for the seventh of eight games this season.