Lundqvist denied offerings from Anthony Duclair, Clayton Keller and Derek Stepan in the shootout and also made 38 saves through regulation and overtime at the Gila River Arena to earn the 424th victory in his career.
Lundqvist moved ahead of Tony Esposito for sole possession of eighth place on the NHL's all-time list for wins by a goalie.
The Rangers (22-14-5) won despite being without leading scorer Mats Zuccarello, who missed the game due to illness. New York produced a comeback effort against an Arizona club that sits last in the league standings and has now lost the last nine meetings between the teams.
Duclair opened the scoring for the Coyotes just past the midway point of the first period with a power-play marker when he pounced on a loose puck during a scramble and slipped a shot past Lundqvist.
It was the ninth goal of the season for Duclair, who is enjoying a bounce-back season after a miserable 2015-16 campaign in which he scored only five times.
Jimmy Vesey replied for the Rangers 5:11 into the second period, first stealing the puck from star defender Oliver Ekman-Larsson, then driving to the net and lifting a short-side effort past Coyotes goalie Antti Raanta.
Raanta, who was traded to Arizona last summer after two seasons with the Rangers in which he served as Lundqvist's backup, made 24 saves for the Coyotes (10-27-6).
Arizona received some good news, as forward Brad Richardson returned after missing four games due to injury.
--Field Level Media
NY Rangers | Arizona | |
Jimmy Vesey 1 | Points | Anthony Duclair 1 |
Jimmy Vesey 1 | Goals | Anthony Duclair 1 |
Jimmy Vesey 0 | Assists | Christian Dvorak 1 |
N/A | Power Play Goals | Anthony Duclair 1 |
N/A | Short Handed Goals | N/A |
Henrik Lundqvist .974 | Save Percentage | Antti Raanta .960 |
Henrik Lundqvist 38 | Saves | Antti Raanta 24 |
Team | Shots | Goals | Power Play | Penalty Kill | Penalty Mins | Face Offs Won |
NY Rangers | 25 | 2 | 0-1 | 1-2 | 4 | 28 |
Arizona | 39 | 1 | 1-2 | 1-1 | 2 | 22 |