Jere Lehtinen, Ladislav Nagy and Loui Eriksson also scored as Dallas improved to 8-1-1 in is past 10 games. Marty Turco made 21 saves for his 30th career shutout.
Mikael Tellqvist stopped 19 shots for the Coyotes, 2-9-2 over their past 13.
Dallas blanked Phoenix for the third time this season and the Stars finished the season series against the Coyotes at 7-1 to move to 98 points, two behind the first-place Anaheim Ducks in the Pacific Division.
In the teams' previous meeting Saturday night, the Stars needed a three-goal third-period rally to get to the shootout, then beat the Coyotes 4-3.