The Avalanche left most of their veterans in Denver so their top prospects could get extra ice time. The Stars used more veterans, but their lineup also included seven prospects.
Dallas took four penalties in the game's first five minutes - three on Jamie Benn - and Barrie capitalized on a 5-on-3 power play at 6:41.
Rookie Colton Sceviour tied it at 1 for Dallas at 10:11 of the opening period, and later poked a loose puck past goaltender Calvin Pickard at 9:18 of the second period to put the Stars in front.
Malone drew Colorado even at 2 at 12:09 of the second, beating Campbell from the left circle on the power play.
Jordie Benn, older brother of Stars forward Jamie Benn, beat goaltender Trevor Cann from the slot 22 seconds into the third period to snap a 2-all tie.
Loui Eriksson and Steve Ott added third-period goals for the Stars (2-0) in their preseason home opener.
Barrie and Malone had two-point nights (each had a goal and an assist), and fellow rookie Gabriel Landeskog finished with a game-high seven hits in his NHL preseason debut.