NEW YORK -- Some fourth-line chemistry and the presence of the NHL's worst team on the other bench were exactly what the New York Rangers needed to get on the right track.

Pavel Buchnevich and Michael Grabner had two goals apiece, and Boo Nieves had three assists as the Rangers dispatched the winless Arizona Coyotes easily in a 5-2 victory Thursday night at Madison Square Garden.

The Rangers had used 11 forwards -- three centers -- the previous two games, but they called up Nieves from AHL Hartford before Thursday game to play center. He made an immediate impact, assisting on the Rangers' second, third and fourth goals to help quell any hopes the Coyotes had of overcoming an early 2-0 deficit.

With the Coyotes (0-9-1) offering little resistance, the Rangers (3-6-2) were able to earn a rare victory.

"I think we meshed really well," Nieves said of his linemates. "Grabner is a really fast player, like me, so it's easy to keep up with him. A guy like Buchnevich can put the puck just about anywhere. They made my transition here pretty easy."

So did Coyotes goaltender Adin Hill, who allowed two soft goals that helped the Rangers coast to a win that included a late empty-net goal by Grabner.

Kreider opened the scoring on a beauty of a goal as Mats Zuccarello was able to thread a no-look pass in front to Kreider, who buried his second goal of the year at 8:01 of the first period.

Buchnevich extended the lead to 2-0 on a stoppable shot from the left-wing boards that got past the Hill's catching glove with 4:03 remaining in the period.

Former Ranger Anthony Duclair cut the lead to 2-1 early in the second period, but Grabner answered 46 seconds later after accepting a precise pass from Nieves in front of the net and faking out Hill to restore the two-goal lead.

"It was a key to the win," said New York goalie Ondrej Pavelec, who stopped 27 shots in his second start of the season to earn his first win. "We get that momentum back right away, and it was huge. That's what we talk about -- if they score the goals, nothing happens and we just stick with the plan."

Any hope of a comeback was quashed when Hill skated to the slot to play a puck, only to turn it over to Nieves. He found a cutting Buchnevich for a deflection that went wide, but with Hill so far out of the net, Buchnevich had time to gather the puck and stuff into the yawning net to put the Rangers on top 4-1 with 6:04 remaining in the second period.

"You can't give them freebies," Coyotes coach Rick Tocchet said. "It's hard because you're chasing the game. ... Their hearts are in the right direction, but when you give (the opponent) a couple of free goals, they think about how we are going to get back in the game. That's what happened tonight."

Arizona's Clayton Keller scored his rookie-leading seventh goal early in the third period. That would be the final goal allowed by Pavelec, who provided the Rangers with a solid performance in what was an oddly crucial late-October game, according to captain Ryan McDonagh.

"Tonight, we wanted to get back to playing the right way and playing high-percentage (hockey)," McDonagh said. "I thought for the majority of the night, we played really well with the puck, and that was the difference."

The Coyotes will once again try for their first win of the season Saturday in New Jersey against the Devils. They hope their relatively strong third period can be a springboard to ending the winless skid.

"We were in the game, and then in the second, they had a little bit of a push," Keller said. "I thought we pushed back, but just had some unlucky bounces there. In the third, we got back to what we were doing, and we started to play our way."

It wasn't pretty, and the Coyotes didn't offer much resistance, but the Rangers found a win that may have helped save their season.

"You look at it as both teams are fighting to get points," New York coach Alain Vigneault said. "You'd have to say that this was a challenging game in the sense that you've got to think that they might be due to win one, and we need the points. I thought we came out well, we played real strong in the first period and responded well in the second."

NOTES: Former Coyotes RW Shane Doan, who retired in the offseason after 21 seasons with the club, joined the NHL's hockey operations department Thursday. Doan is expected to stay in Arizona with his family. ... Coyotes C Derek Stepan, who spent nine seasons in the Rangers organization before a trade to Arizona in the offseason, was given a warm welcome from fans after a video tribute was shown on the scoreboard. "Mentally I wasn't sharp," he said, "It was just hard to stay focused." ... Rangers LW Rick Nash played in his 1,000th career regular-season game. "It's a special night I'll never forget," he said. ... Rangers D Marc Staal played in his 700th career regular-season game.