TORONTO - The Islanders know well what awaits them Tuesday night at the Coliseum.

They realized a little late Monday night that there was business to take care of here, but they did just in time.

John Tavares scored on a terrific individual effort with 21.8 seconds left in overtime for a 4-3 Islanders win over the sinking Maple Leafs, salvaging a win from a game in which the Isles twice trailed by two goals in the third period. They can take that back home to their date with the Rangers Tuesday night.

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"It's certainly a lot better to go back home with some momentum," Travis Hamonic said. "It's probably as big a game as we've had all season and we're all well aware of it. We'll be prepared."

The Isles didn't seem too prepared through 40 minutes against a Maple Leafs team stumbling toward the finish line of a brutal season. Talented Leafs center Nazem Kadri was a healthy scratch after arriving late to Sunday's practice and the Islanders appeared to arrive late to this game, giving up odd-man rushes and playing without much flow.

That translated to a 2-0 deficit after goals by David Booth in the first period and Peter Holland in the second, both on odd-man rushes.

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"We were flat at the start for some reason," coach Jack Capuano said. "We had to get back to what we've been doing."

And they had to do it without one of their mainstays, Nick Leddy, who left the game after the second period. He appeared to take a slash to the back or leg on a second-period scoring chance and missed a period for the first time all season.

Capuano made a switch at forward to start the third period, putting newest Islander Tyler Kennedy on Tavares' right side. It worked almost immediately, with Kennedy snapping a wrist shot past Jonathan Bernier off a drop pass from Tavares just 1:32 into the period.

"That one gave us some life," Tavares said.

Less than five minutes later, Hamonic had a shot blocked by James van Riemsdyk, who corralled the loose puck for a semi-breakaway and a wrist shot past Michal Neuvirth at 6:06 to put the Isles down by two again.

But two quick strikes brought them even. Frans Nielsen attacked the Leafs' net on a power play and deposited Anders Lee's pass at 9:58. Only 30 seconds later, local kid Casey Cizikas made a terrific deflection of Hamonic's shot for a 3-3 game.

Neuvirth (22 saves) came up with big glove saves on van Riemsdyk and Morgan Rielly in the final minutes of the third and Bernier turned aside 16 Islanders shots in the final frame.

As the seconds wound down in OT, Tavares gained the Leafs' zone, eluded Richard Panik and undressed Rielly with a slick move to the net before sliding the puck through a crowd for his 33rd goal, league-leading 72nd point and fourth OT winner, also tops in the NHL.

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And, perhaps as important, a healthy dose of good feeling and relief heading into Tuesday night's Coliseum showdown. The second-place Rangers sit three points back in the Metropolitan Division and have four games in hand.

"You can't look past anyone," Tavares said. "Points are so huge, they're all valuable now. You can't take anyone for granted."