Tavares followed Frans Nielsen's goal in the opening round of the tiebreaker with one of his own, and Evgeni Nabokov stopped Marian Gaborik and Rick Nash to give the Islanders the elusive win. They had dropped eight straight at Madison Square Garden, including a loss there last week.
The Rangers (7-5-1) squandered a 2-0 lead and had their three-game winning streak snapped.
Dan Girardi and Gaborik staked the Rangers to the lead in the first period against Nabokov. Carl Hagelin tied it in the second.
Martin Biron gave Rangers' workhorse goalie Henrik Lundqvist a break by making just his second start of the season. He was touched for goals by Colin McDonald, Tavares and Brad Boyes in the second when the Islanders grabbed the lead.
Nabokov made 36 saves through overtime, and Biron had 28. Both teams had four shots in overtime. The Islanders' Michael Grabner pushed the puck wide of the net on a breakaway with 10 seconds left
Whatever Islanders coach Jack Capuano told his club during the first intermission worked.
McDonald got the Islanders' rally going 31 seconds into the middle frame when Casey Cizikas found him with a pass from behind the Rangers net for a quick shot that cut the deficit to 2-1.
The Rangers had a chance to stretch their lead a few minutes later when Eric Boulton and Nielsen were called for penalties 1:27 apart, giving the Rangers' struggling power play a 5-on-3 edge for about a half-minute.
But the Islanders killed both infractions, and used that momentum to further fuel their offense.
Just seconds after Nielsen left the box, the Islanders got even on Tavares' eighth goal.
Rangers defenseman Anton Stralman lost the puck as he tried to go deep into the offensive zone, and the Islanders turned that into a 2-on-1 rush. Tavares raced up ice and fired a shot that found the net after smacking off Biron's glove at 6:45.
The crowd had barely absorbed the sting of the Rangers' second blown multigoal lead in two games when the Islanders struck again.
[to top of second column]
It took only 40 seconds for Boyes to turn a pass from defenseman Lubomir Visnovsky into a quick shot from the right circle that made it 3-2.
The offense was a reversal of fortune for the Islanders, who came in with one of the worst goal differentials in the NHL while playing 5-on-5. They scored four power-play goals in a home loss to Carolina on Monday and netted none at even strength.
That had Rangers fans chanting "Hen-rik, Hen-rik" toward Lundqvist, who was sitting on the bench.
The Rangers rebounded from the blown 3-0 lead at Boston in the third period on Tuesday and pulled out that win in a shootout.
They showed resolve again, and they did it with their much maligned power play. The Rangers had connected for only four goals in 44 man-advantage situations this season before Thursday, and were aided by a favorable video review.
A dump in bounced in on Nabokov, and Hagelin kicked the puck with his skate. Hagelin stood tall as he crowded Nabokov in the crease, and managed to nudge the puck into the corner of the net with his stick to tie it 3-3 at 11:14.
Capuano was irate on the Islanders bench and voiced his displeasure to both referees after the goal was confirmed by a video review.
The Rangers broke out with two goals in the first period. Girardi beat Nabokov at 3:36 for the defenseman's first goal of the season.
Gaborik, on his 31st birthday, doubled the Rangers' lead at 11:28 after an Islanders turnover.
NOTES: Rangers C Brian Boyle returned to the lineup after being a healthy scratch the previous three games. Boyle recorded only one assist and was a minus-3 in the first nine games of the season. Chris Kreider sat out. ... Nabokov has started 11 of the Islanders' first 13 games. ... Hagelin has scored four goals in three games
Press; By IRA PODELL]
Copyright 2013 The Associated
Press. All rights reserved. This material may not be published,
broadcast, rewritten or redistributed.