Adam Burish carried the puck up the right side and centered a pass to Morrow, who skated hard to the net and beat goaltender Craig Anderson for his third preseason goal.
Colorado's Kevin Porter struck from close range at 8:43 of the third period to break up a scoreless game.
Mike Ribeiro countered on the power play at 13:32, tying it at 1.
Kari Lehtonen made 22 saves for the Stars. Anderson stopped 21 shots.
Dallas (3-2) wraps up its preseason schedule Saturday night at St. Louis and opens the regular season at New Jersey on Oct. 8.
Colorado (2-4) plays its final preseason game Saturday night against Los Angeles in Las Vegas. The Avs get the regular season underway at home on Oct. 7 against defending Stanley Cup champion Chicago.