While the Rangers were able to continue theirs the last time out, the Coyotes' costly and disheartening defeat in their most recent outing could come back to haunt them.
New York seeks its fourth straight victory when it faces a Coyotes team that's looking to get back to its winning ways Monday night.
The Rangers (39-29-4) won for the second time in as many days Saturday, beating New Jersey 2-0 behind Henrik Lundqvist's 21 saves. Lundqvist earned his 50th career shutout to pass Ed Giacomin for the team record and moved New York three points up on Washington and four on Columbus - which the Rangers defeated 2-0 on Friday - for the third and final postseason berth in the Metropolitan Division.
''We are still in a position where we are fighting for our lives,'' Lundqvist said. ''We have to keep pushing ourselves and have the mindset that every point could be the difference right now. It's going to be until the end, the last game. A lot of it is going to be mental, how we push each other and approach every game as a must win.''
Lundqvist has held opponents to two or fewer goals in 16 of his last 23 games, and he is 6-2-0 with two shutouts in his last eight starts.
''He's been tremendous,'' defenseman Ryan McDonagh said. ''He has been in this position before. He is the leader on the back end, the backbone of our team. You can see it. He is talking a lot and making great efforts on second and third pucks around the crease. We need him to continue.''
Lundqvist will continue to get the call despite the Rangers playing for the third time in four days Monday, making his fifth straight start and 12th in the last 13 games.
Phoenix (34-26-11) looked to be on its way to a fourth consecutive win Saturday, taking a 2-1 lead into the third period against Boston. The Coyotes, though, allowed three goals in the final 20 minutes and suffered a 4-2 loss as the Bruins won their 12th in a row.
Phoenix came into the game with seven wins in its previous nine. It's clinging to the final Western Conference wild-card spot, two points up on Dallas, which won Saturday and has a game in hand.
"A disappointing one to let points slip away," captain Shane Doan said.
The Coyotes hadn't allowed four goals in the past nine games, but wilted under Boston's sustained offensive pressure in the third.
"It was a huge two points for us, we didn't get it, so it's gonna be a huge road trip for us here," said defenseman Oliver Ekman-Larsson, whose spectacular goal 39 seconds into the second period gave the Coyotes the one-goal advantage heading into the third.
Phoenix's trip also takes it to Pittsburgh and New Jersey. The Coyotes have won three of four on the road, but they've dropped four in a row at Madison Square Garden, the last two in shootouts.
Phoenix did defeat New York 4-1 in the teams' season opener Oct. 3, getting a hat trick from Radim Vrbata and 23 saves from Mike Smith.
Vrbata has four goals and an assist in his last three games in the series.