Colorado's Semyon Varlamov stopped all three Stars shots in the shootout after O'Reilly lifted the puck over Dallas' Kari Lehtonen and in off the crossbar.
Nate Guenin had a career-high three points with a goal and two assists for the Avalanche. They rallied from deficits of 3-1 and 4-3 in the third period.
Cody Eakin had two goals and an assist, but the Stars lost their fifth straight game (0-3-2) They also were 0-3-2 against Colorado this season.
For Colorado, Tyson Barrie also had a goal and two assists. Gabriel Landeskog had one of each, Matt Duchene assisted twice and Jarome Iginla scored a goal.
Jason Spezza and Antoine Roussel also scored for Dallas.