Doan picked up his first of the game early in the second period when he converted a centering pass from Niko Kapanen at 44 seconds. He then added an insurance goal at 14:47 of the final period.
Jovanovski scored the tying goal for the Coyotes, on the power play at 10:52 of the second, and Mueller had the go-ahead score at 18:16. Phoenix rookie Hanzal made it 5-3 at 7:17 of the third period.
After Lundqvist's second goal pulled the Stars within one, Doan restored the two-goal margin. Conner closed the scoring with 17 seconds left.
Lundqvist's first goal, when he converted a centering pass from Chris Conner at 1:21, gave the Stars a 1-0 lead. Hagman scored short-handed at 3:44.
Carcillo cut the margin in half as he flipped in a goalmouth scramble past Marty Turco at 5:13.
Because of five consecutive minors, Phoenix skated short-handed the final eight minutes of the first period, including three 5-on-3 disadvantages. In that span, Dallas managed one goal when Miettinen put the puck just under cross bar from 15 feet out at 18:48.