Blair Betts got the Rangers even in the first period, and defenseman Dan Girardi added insurance with a power-play goal in the third. Henrik Lundqvist returned to the net for the first time in five days and made 35 saves for his NHL-leading 13th win.
Gomez sealed it by scoring into an empty net with 27.9 seconds left Enver Lisin scored and Ilya Bryzgalov stopped 32 shots for the Coyotes, 0-4-2 during their slide. It is their worst stretch since another six-game losing streak from Feb. 7-19, 2007. They will finish a four-game trip at Columbus on Wednesday.
The game was played cleanly with only one fight and three minor penalties whistled. The Rangers split their two power-play chances, and the Coyotes were 0-for-1.
Girardi took a pass from Zherdev at the blue line and fired a shot through traffic to give New York a 3-1 lead 7:37 into the third.
The Rangers fell behind 1-0 for the eighth straight game when Lisin scored his second of the season 4:08 in. Lisin, playing in his fourth game with the Coyotes and second since being recalled from San Antonio of the AHL, took a pass in front from Olli Jokinen and slipped a shot under Lundqvist's pad.
New York nearly broke its first-goal blues moments earlier, but Dubinsky's drive from the high slot slammed off the crossbar behind Bryzgalov. Dubinsky found the range in the second period with his first goal since a game-winning tally at Columbus on Oct. 24.
Betts did tie it with 6:27 left in the first period, showing the skills of a goal scorer that are not associated with the effective checking-line forward. He had just come on the ice on a shift change and took a crisp pass from Zherdev, who found him cutting down the middle of the Phoenix zone.
Betts cut to his left with the puck on his backhand and then deftly moved around Bryzgalov before pushing the puck into the open side with his forehand. It was his third goal in 24 games after he netted only two all last season.
Dubinsky, who fought Coyotes enforcer Daniel Carcillo in the first period, made it 2-1 at 1:15 of the second with a wraparound goal. It was actually scored when Phoenix defenseman Ed Jovanovski gave the puck its final push over the line as he tried to get it out of the crease.
Notes: The Rangers had gone seven games without scoring in the first period. ... Coyotes coach Wayne Gretzky, who played the final game of his Hall of Fame career at Madison Square Garden on April 18, 1999, had 29 goals and 105 assists in 114 games with the Rangers. ... Gomez centered a new line between Chris Drury and Ryan Callahan. ... Phoenix held a 16-11 shots advantage in the first period. ... The Coyotes are 3-for-33 on the power play during their skid. ... Zherdev has 201 career points.