Travis Morin, Trevor Daley and Morrow followed Gagnon with first-period goals against rookie goalie Jake Allen as the Stars (2-1) dominated the period with a 13-5 edge in shots.
Gagnon's goal off a wrist shot at 10:19 gave Dallas the lead. Morin struck on a rebound 13 seconds later, Daley connected at 13:15, and Morrow scored at 14:45 to make it 4-0.
Nikita Nikitin's power-play goal got the Blues scoring underway at 3:35 of the second period. Stefan Della Rovere's even-strength goal at 7:27 cut it to 4-2, but Morrow countered at 18:26 of the second period to restore Dallas' three-goal edge.