Kessel had two goals for the second straight game against New York, though the Maple Leafs lost 3-2 in a shootout Wednesday to give the Rangers a split in a home-and-home series.
The speedy winger snapped a nine-game goal slump with two goals Monday, including the game-winner in Toronto's 4-3 win at home, then had both goals at Madison Square Garden to help keep Toronto (22-13-5) firmly in the fifth seed in the Eastern Conference, five points clear of sixth with eight games remaining.
"He's been playing good all year and now he's on the receiving end of some good plays and he's putting in his chances," said linemate Tyler Bozak. "He's been good for us all year, now it's just starting to reward him."
Despite the loss, the Leafs stayed on pace to make the post-season for the first time since the spring of 2004, which would end a seven-season playoff drought that is the longest in franchise history.
"At the end of the day we battled hard for a point and it's a very valuable point and we'll just keep working," said Toronto goalie James Reimer, who finished with 26 saves in his sixth straight start.
Mats Zuccarello scored the only goal in a shootout while Carl Hagelin and Ryan McDonagh had a goal and an assist each in regulation for New York (20-6-4).
The Rangers earned two badly needed points and moved into a three-way tie for sixth in the East along side the Ottawa Senators and cross-town rivals the New York Islanders, who they will next meet on Saturday.
Henrik Lundqvist made 23 saves after allowing four goals Monday in a uncharacteristically mediocre performance. The all-star hadn't given up more than three goals since Feb. 26 against Winnipeg.
"I didn't feel that sharp in Toronto," said Lundqvist. "But you just have to fight for it and tonight I felt better. I was making better decisions and I was reading the plays better. They're still a tough team to play. They come with a lot of speed and lot of delayed plays.
Kessel scored on Toronto's first shot of the third period when Dan Girardi's turnover led to a Kessel and James van Riemsdyk 2-on-1. With the two Leafs streaking down the ice, Kessel converted van Riemsdyk's pass to tie the game 2-2 at 8:05.
Ryan Callahan almost had the go-ahead goal with just over four minutes left to play, but Reimer shut the door on his wraparound attempt and the playoff-atmosphere crowd roared with disbelief.
Nazen Kadri had a wide-open net in overtime, but Lundqvist got an arm out just in time to deflect the puck.
Bozak, Kadri and Mikhail Grabovski took shootout attempts for the Leafs. Toronto hasn't been strong in this department this season. All five of the Leafs shootout appearances have come up short on the extra point.
"Shootout is one of those things, it seems to haunt our hockey club," said Leafs coach Randy Carlyle. "There's five extra points we've lost. It's not a healthy stat, it's an area we'd like to improve on.
"I thought our goalie gave us a chance, but if you don't score a goal in the shootout you're not going to win many of them."
The Leafs came out aggressive in the second and just 20 seconds after Clarke MacArthur was stopped on a breakaway, Callahan turned around to clear the puck when Kessel stole it right off his stick and quickly put it past Lundqvist for the game's first goal at 1:42 and his 13th of the season.
"Sometimes that's how it goes for goal-scorers," said van Riemsdyk. "There's streaks were you can't seem to buy one and then everything you touch goes in. He's a really talented played and obviously it was just a matter of time before it started to go in for him."
The Rangers didn't register a shot until midway through the second with the Leafs down a man. Toronto's penalty kill — third overall in the league — went to work and kept the puck out their zone to end the threat.
"The (PK) been on pretty much the whole year," said Bozak. "Jay McClement is a huge part of that, he plays most of the minutes. Also our goalies, they have to be the best penalty killer out there. They've been standing on their heads for us."
But New York tied the game 1-1 at 10:55 when Hagelin, waiting at the side of the net, received a fortuitous rebound and slammed in his first goal in 11 games.
The Rangers went ahead 2-1 at 16:43, with Callahan screening Reimer, McDonagh slipping around Kadri and blasted in a wrist shot from the blue-line that cleared traffic. The Blueshirts finished the period with a 10-5 edge in shots.
Kessel looked in dangerous in the first, taking Bozak's backhanded pass from behind the net and putting a point-black shot on Lundqvist with six minutes left in the frame. Reimer proved equally up to the task at the other end as the Rangers swarmed, with Brad Richards and Derek Stepan taking turns testing the Leafs goalie.
Toronto outshot the Rangers 11-8 in the opening period.
The Leafs are next in action against another Original Six opponent — the Montreal Canadiens — at home on Saturday night.
Notes: Toronto forward Joffrey Lupul did not make the trip and missed his third straight game after suffering an upper body injury in last Thursday's loss in Philadelphia. Lupul has only played in 10 games this season but is still 10th on the Leafs in points with eight goals, six assists. Matt Fratin, Ryan Hamilton, Jake Gardiner and Michael Kostka were also scratched. ... The Rangers were without defenceman Marc Staal, who has missed 18 games after taking a puck in the eye but skated with the team on Tuesday.