GLENDALE, Ariz. - After 40 sluggish minutes in the desert Saturday night, the Rangers woke up.

With the score tied at 1 in the final game of this three-city trip, the mood in the Rangers' locker room was unsettled. "We weren't happy," Marc Staal said. "They outchanced us by a lot. They were getting a lot of looks we don't ordinarily give up."

Then the Rangers came alive with four goals in the third period to beat the Coyotes, 5-1, for their third straight win.

It was coach Alain Vigneault's 500th victory, tying him for 18th place with Toe Blake.

The Rangers took the lead for good at 1:19 of the third. Kevin Klein, with his second assist of the night, sprung Rick Nash, who took three strides and unleashed a bullet that went off the crossbar and in behind goaltender Mike Smith for his NHL-leading 35th goal of the season.

Cam Talbot (34 saves), who was excellent and has won four of his last six starts, stepped up and denied Toby Rieder's penalty shot at 6:20 after the Arizona right wing was tripped from behind by John Moore.

"Huge momentum swing," Nash said. "Cam seems to keep stepping up for us in the third periods." Talbot said that one thing he addressed with goaltending coach Benoit Allaire after a shaky game in Toronto on Tuesday "was trying to attack the puck instead of letting the puck come to me, some of those goals I was gliding a little backward and it's tough to make saves when you're not square to the shooter. Thought I made a pretty good adjustment the last two nights."

The dagger came at 10:06 with Derick Brassard in the box for a delay-of-game penalty with the Rangers ahead 2-1. After Oliver Ekman-Larsson broke his stick in mid-ice, Kevin Hayes skated down the left side with the puck on a two-on-one. Ekman-Larsson skated back hard and caught up, then went down to the ice to try to stop Hayes from centering a pass. Hayes danced around Ekman-Larsson as he slid by, then walked in and beat Smith at 11:54.

"I actually wanted to dish [it] to [Tanner] Glass," Hayes said. "[Ekman-Larsson] went down early and I waited him out."

Staal and Lee Stempniak scored the last two goals late in the third period.

In the second period, Chris Kreider blazed down the left side into the zone, skated past Michael Stone and tucked the puck between Smith's pad and the right post with his backhand at the 55-second mark for a 1-0 lead. It was Kreider's 13th, with assists going to Derek Stepan and Klein.

Just after the Coyotes missed an open net on a rebound, Antoine Vermette, a subject of trade rumors, buried his 13th of the season for a 1-1 tie at 6:33.

Stepan sprung Kreider again, this time down the middle, but Smith was immovable.

After two periods, the shots on goal were almost even: The Rangers had 20 and the Coyotes had 21.

In the first period, the Coyotes had more chances than the Rangers but had some shots blocked and missed the net with open looks. They also didn't connect on two power plays, the first at 1:20 when Carl Hagelin was whistled for embellishment, falling with Connor Murphy sticking him from behind.

Smith, who was in the net for a 4-2 loss to the San Jose Sharks here on Friday night, stopped a couple of close-in tips -- by J.T. Miller and Martin St. Louis -- and then stopped Dom Moore's jam attempt in the crease. Talbot, making his sixth straight start with Henrik Lundqvist sidelined with a blood vessel injury, made a quick left pad save on a one-timer from Vermette as one power play with Miller in the box on a too-many-men-on-the-ice penalty at 10:11 was ending.

Talbot is expected to make his seventh straight start and first against the Islanders this season Monday night.