WATCH: [All Rangers vs. Coyotes highlights]
Jimmy Vesey scored for New York (22-14-5), which has won its past nine games against the Coyotes, and Mika Zibanejad scored the only goal in the shootout. The Rangers are 6-2-2 in their past 10 games.
Lundqvist, who saved all three shootout attempts by Arizona, passed Tony Esposito for eighth place on the NHL wins list with 424.
"I felt really good," said Lundqvist, who made 10 saves in the first period, when the Coyotes controlled possession. "With the way the first period went, it was a lot of chances and they're a quick team.
"They have a lot of young guys that are still learning when to go and when to be smart but you can see the skill and the speed and they work hard. They work really hard and we got outworked in the first."