Updated

New York, NY (SportsNetwork.com) - Ryan McDonagh scored on a rebound 1:56 into overtime and the New York Rangers pushed their winning streak to four games in a 4-3 victory over the Phoenix Coyotes on Monday.

The Rangers tied the game and won it against backup Coyotes goaltender Thomas Greiss after starter Mike Smith suffered an apparent leg injury late in the third period.

McDonagh was all alone in front of Greiss for a rebound off Dan Girardi's slap shot from above the right circle. Girardi had tied the game with 3:28 left in regulation when he deflected McDonagh's point shot.

The victory came after the Rangers celebrated Henrik Lundqvist setting the franchise wins record. It moved them one point ahead of Philadelphia for fifth place in the Eastern Conference.

Brad Richards and Derick Brassard also scored for New York and Lundqvist made 18 saves.

Oliver Ekman-Larsson, Jeff Halpern and Kyle Chipchura scored for the Coyotes, who have lost two in a row for the first time since a four-game slide that spanned the Olympic break.

"That's a team I know really well and usually when they have a lead they keep the lead," said Rangers coach Alain Vigneault.

This case was different.

The Coyotes, clinging to the No. 8 seed in the Western Conference, lost Smith after Brassard fell on top of him the crease.

Brassard was nudged by Coyotes defenseman Derek Morris and Smith's legs bent awkwardly underneath him. The goaltender grabbed his right leg and smacked his blocker against the inside of the net. In obvious pain, he had to be helped off the ice.

The Coyotes did not have an immediate word on his condition other than to say it was a lower-body injury.

"It was a tough situation. I would like to see us be a little tougher in front of him, but it is what it is," said Phoenix coach Dave Tippett.

Smith had 25 saves and Greiss stopped seven. Tippett said Greiss was scheduled to play Tuesday at Pittsburgh anyway and "that won't change."

Richards scored 6:10 into the second period, getting his stick up to deflect a point shot by Carl Hagelin past Smith from in front of the crease.

Brassard tied the score at 2-2 less than five minutes later when he ended up with his own rebound on the low right side and beat Smith on a sharp-angle shot.

But the Coyotes regained the lead at 3-2 when Chipchura threw the puck toward the crease from near the left boards and Rangers winger Chris Kreider deflected it into his own net at 16:51 as he skated near the crease.

The Rangers honored Lundqvist in a pre-game ceremony six days after he set the franchise record for wins with his 302nd, passing Mike Richter.

Lundqvist, known for his guitar chops, received a powder blue Gibson Les Paul Custom from teammates and a mask emblazoned with the number 302.

Then, he gave up two goals in the first 8 minutes and 22 seconds.

Ekman-Larsson beat him with a wrister from the right circle on a power play 4:40 into the game and Halpern scored on a one-timer from the low slot to make it 2-0.

Game Notes

McDonagh had two assists ... In their only other meeting of the season, the Coyotes beat the Rangers 4-1 in both teams' season opener, snapping a three- game losing streak in the series ... Phoenix began a three-game road trip ... The Rangers will play Philadelphia at home on Wednesdays.