NEW YORK -- If the New York Islanders were supposed to lose Thursday night because it would have been better for their postseason matchup, someone forgot to tell their goaltender.

Thomas Greiss stopped 36 shots and was less than three minutes from a shutout as the Islanders dispatched the New York Rangers 4-1 at Madison Square Garden.

The Islanders claimed third place in the Metropolitan Division and dropped their New York rivals into the first wild-card spot in the Eastern Conference playoffs.

Conventional wisdom says finishing higher in the standings is better, but that might not be true in this case. Whichever team finishes third in the Metro will draw the Pittsburgh Penguins, who have won eight straight and 14 of 15, while the wild-card team will face the largely inexperienced Florida Panthers.

The Islanders and Rangers are tied with 99 points, but the Islanders have two games remaining while the Rangers have one left.

"We play to win," said Islanders captain John Tavares, who had a goal and an assist. "We approach each game of the season the exact same. We want to keep climbing. We show pride as a group, and when you play against your rival, it's a lot of fun, so we went out there to play to win."

Through nearly 34 minutes, it appeared as though nobody wanted to win, as both teams were playing scoreless, lifeless hockey.

That was before left winger Shane Prince made it 1-0 on a deflection goal with 6:32 remaining in the second period. He then assisted on a goal by center Casey Cizkias about five minutes later.

Center Frans Nielsen increased the lead to 3-0 with 14.8 seconds remaining in the second with a power-play goal, which led to Rangers goaltender Henrik Lundqvist being pulled to start the third period after allowing three goals on 16 shots.

The scoring outburst would not have been possible without Greiss' key stop on Rangers left winger J.T. Miller, who was denied from point-blank range when it was still just 1-0 Islanders.

"I don't think we played too well in the second period," said Nielsen, referring to the Rangers' 16-9 edge in shots during the middle frame. "(Greiss) had that huge save right there, then 20 seconds later, it's in their net. That was a game-changer right there, for sure."

The Islanders have won three straight since coach Jack Capuano called out individuals -- a rarity in the NHL -- for a lack of effort after a 5-0 home loss to the Penguins.

"The guys are playing hard," Capuano said. "We went through a stretch where we lost our identity a little bit."

The Rangers, much like the Islanders, were playing without some key players Thursday.

"We've had injuries before," Rangers coach Alain Vigneault said. "We have to find ways to get it done. We didn't give up much tonight. We gave up a couple quality chances in the second and third there, but we didn't give up much, to be honest."

The Rangers had won two straight before Thursday, but they are just 2-3-1 in their past six games. Lundqvist has been yanked twice in the past four games and has just one game remaining -- a Saturday afternoon contest at home against the Detroit Red Wings -- to right himself before the postseason.

"You try to get good habits," Lundqvist said. "You want to prepare the same way. You want to get ready for a good game. In the back of your head, you start focusing on next week and what's ahead. But at the same time, you want to make sure you work on your game and try to play as good as you can."

The Islanders appear to be doing that. It is just matter of whether they have to carry it over against the Penguins or Panthers.

"We're playing good right now," Nielsen said. "We're winning, and I think we've got confidence."

NOTES: Islanders D Calvin de Haan returned after missing Tuesday's game with an injury he sustained Monday. ... Islanders RW Cal Clutterbuck (undisclosed), LW Matt Martin (upper body) and D Brian Strait (upper body) did not play. ... The Rangers were without D Ryan McDonagh (hand) and D Dan Girardi (upper body). McDonagh will miss the final game of the regular season on Saturday and could miss postseason games. Girardi, who was injured in the final minutes of Tuesday's game, is considered day-to-day. ... Rangers D Dan Boyle and C Kevin Hayes, who did not play Tuesday, were back in the lineup. ... Rangers C Oscar Lindberg was a healthy scratch.