Mike Zigomanis scored the winning goal and Steven Reinprecht added a pair of assists for the Coyotes, outscored 8-1 in their first two exhibition games -- both on the road.
Eric Lindros and Jaroslav Modry scored for the Stars, who fell to 1-2 while playing their third game in three nights.
Modry tied it at 2 on a power-play goal from the right circle against David LeNeveu with 11:11 remaining. But Zigomanis, after whiffing on his initial shot, beat Mike Smith from the low slot with 8:44 to go for a 3-2 Coyotes lead.
Nolan had given Phoenix a 1-0 lead 88 seconds into the game on a rebound of his own shot. Lindros tied it at 18:38 of the period when he backhanded a low shot to Curtis Joseph's left.
Nolan made it 2-1 at 4:10 of the second period on another rebound, pushing a loose puck past Dan Ellis from the top of the crease.
Dallas just missed on a pair of opportunities to tie later in the second. Modry bounced a shot from the left off the crossbar with at 10:48, and Mike Modano missed a breakaway attempt off the right crossbar with 4:13 left in the period.