Conor Garland and Nick Schmaltz scored on the Coyotes' first two attempts against Robin Lehner in the shootout, and Arizona rallied from two goals down to beat the Chicago Blackhawks 4-3 on Sunday night.
Only Patrick Kane connected against Darcy Kuemper in the tiebreaker as the Coyotes improved to 5-2 in shootouts this season and finished a 3-1 road trip.
With 40 points, Arizona is tied for first in the Pacific with Edmonton, which lost 3-2 to Buffalo in overtime on Sunday.
Garland got his team-leading 12th goal in regulation, and Carl Soderberg and Christian Fischer also scored. Kuemper finished with 26 saves through overtime.
Jonathan Toews has a goal and two assists for his first three-point game this season. Alex DeBrincat and Dominik Kubalik also scored for injury-depleted Chicago, which played beyond regulation for the third straight game following an overtime win at Boston on Thursday and a shootout win at New Jersey the following night.
Lehner had 44 saves - including several sensational ones - but he lost for the first time in six career games (5-0-1) to Arizona.
A Vezina Trophy finalist with the Islanders last season, Lehner has been solid in net for Chicago so far, but is 0-3 in shootouts with the Blackhawks and 8-23 in the tiebreaker for his career. He last won a shootout on March 8, 2018, while he was with Buffalo.
Toews opened the scoring 53 seconds in. He connected on a backhand deflection of Calvin de Haan's soft cross-ice feed, despite being tied up with defenseman Jason Demers.
DeBrincat's power-play goal at 8:40 made it 2-0. The forward slipped behind Arizona's defense on the left side, took Kane's feed, then burst to the net and beat Kuemper high on the glove side.
Arizona cut to 2-1 at 11 minutes from a goalmouth scramble when Christian's Dvorak's feed from the left side of the net ticked in off Fischer's skate. Kubalik's midair deflection of Connor Murphy's shot from the left point with 2:05 left in the first restored Chicago's two-goal lead.
Garland and Soderberg scored power-play goals in the second to tie it at 3. Garland trimmed it to 3-2 at 6:32 on a wrist shot from the slot.
Chicago rookie defenseman Dennis Gilbert and Demers squared off in a free-swinging fight at 7:01. Gilbert was assessed an extra minor penalty for instigating, as well as a 10-minute misconduct.
Soderberg knotted it at 3 on the ensuing man advantage at 8:53 when his pass from right circle deflected off Chicago' defenseman Slater Koekkoek's stick and over Lehner's shoulder.
Lehner robbed Clayton Keller with a flashy glove save at 9:19 of the scoreless third to keep it tied. Keller was alone at the low edge of the right circle during Arizona's fifth straight power-play when he fired and Lehner reached to grab the shot.
The Blackhawks are at Vegas on Tuesday night to start a three-game trip.