GLENDALE, Ariz. -- Anttim Raanta came within 5 seconds of his second shutout in three games this season.
And it didn't seem to bother him that he didn't quite make it.
Rantaa saved the first 39 shots he faced before the late goal and the New York Rangers won their fifth in a row with a 4-1 victory over the Coyotes on Saturday night.
"Without a doubt he was excellent," New York coach Alain Vigneault said.
Rantaa, backup to first-team goalie Henrik Lundqvist, has allowed two goals in his three games and has the Rangers' only shutout of the season.
"Honestly, I won the first time on the road (since) 2014 in January," he said. "I lost all the games last year on the road, so I really didn't care about the shutout."
Jesper Fast, J.T. Miller, Chris Kreider and Kevin Hayes scored for the Rangers. The Miller and Kreider goals went through the legs of goalie Mike Smith, leading to a change in net for Arizona.
The Coyotes foiled Raanta's bid for his second shutout when Shane Doan scored on a power play with a rebound shot 4.6 seconds from the finish.
"There was lots of luck today so I think they deserved that one," Raanta said. "If you give a rebound and he can shoot it straight through the top shelf, it's like `What are you going to do?' Just laugh about it a little bit and try to save it next time."
Arizona had a third-period goal by Martin Hanzal waived off after a video review showed his stick was above the crossbar when he knocked the puck in after it bounced off Raanta.
New York improved to 10-2-2 and is 4-0 in the second of games played on consecutive nights this season. The Rangers won at Colorado 2-1 on Friday night.
"The last 10 minutes they had some Grade-A chances and he (Raanta) made some unreal saves," Vigneault said. "Obviously goaltending is a big part of a team winning and we got the better goaltending tonight."
The Rangers have won five straight, and eight of the last nine, against Arizona. New York's 22 points are second only to Montreal's 27 in the Eastern Conference.
Arizona was outshot 14-13, missing several chances in the first period and the Rangers led only 1-0. The goal came when Fast redirected the waist-high puck on the shot from Dan Girardi.
New York broke it open with three goals in the second period, the first two a 2 1/2-minute span.
Miller's goal came when the puck glanced off his skate and through the legs of Smith. Moments later, Kreider's shot went through the goalie's legs and that was enough for coach Dave Tippett, who replaced Smith with Anders Lindback.
"We've seen too many like that," Tippett said of Kreider's goal.
So he pulled Smith.
"We needed to change up," Tippett said. "You give up two goals, you're deflated. You've got to try to change something, so that's what we did."
New York got a power-play goal from Hayes against Lindback to make it 4-0. The goal came during a double-minor four-minute high-sticking penalty against Arizona's Brad Richardson.
Smith was pulled for the second time in three games and third time this season.
Longtime Coyote Keith Yandle, traded to the Rangers last February, had an assist on Hayes' goal.
Arizona's 40 shots were a season high.
Notes: Arizona D Nicklas Grossmann, who had two goals in win over Avalanche on Thursday, left the game in the second period with a lower body injury. ... Rangers were without LW Rick Nash for the second straight game due to back tightness. ... Arizona C Antoine Vermette (lower body) was out for the fifth time in six games. ... Lundqvist, who sat out the game after playing Friday night, needs one more game to pass Mike Richter for most overall appearances by a Ranger goaltender in franchise history. ... Since the start of last season, New York is 23-6-5 against Western Conference foes. ... The Coyotes and Rangers met for the second and final time of the season. Rangers won in New York 4-1 on Oct. 22. ... Yandle played parts of nine seasons with the Coyotes (2006-14)