Mike Smith stopped all 17 shots he faced to lead Phoenix in a 2-0 victory over Dallas on Saturday.
Smith also picked up his first win of the season and first shutout since last April.
Nick Johnson and Mikkel Boedker provided the tallies for the Coyotes, who shook off a pair of losses beyond regulation earlier in the week to win their second home game in the last three attempts.
Richard Bachman's first start of the season turned into a 32-save defeat for the Stars, who lost for the fifth time in six contests.
Johnson wristed one home from between the circles and the Coyotes netted the first score of the game with 8:03 left in the second period. Lauri Korpikoski set up the strike, carrying up the left-wing before a perfect dish into the middle of the ice.
Boedker roofed a shot from in close on a power play with 2:47 played in the third period, and Smith shut the door with eight saves in the final 20 minutes.
Smith made six stops and Bachman was true on 11 chances in a scoreless first period.