Stastny faked Joey MacDonald then beat him with a backhand. Wojtek Wolski also scored for Colorado in the shootout. Jiri Hudler had Detroit's lone shootout goal.
Brett McLean and Mark Rycroft scored in regulation for the Avalanche, while Nicklas Lidstrom and Hudler scored for the Red Wings.
Hudler put the Red Wings (0-1-1) ahead 2-1 at 3:39 into the third period. McLean tied it for the Avalanche (2-0) at 7:24.
Lidstrom opened the scoring with a power-play goal with 4:04 left in the first period. Colorado evened it on Rycroft's power-play score with 9:51 remaining in the second period.
Chris Osgood was in goal for the first two periods for the Red Wings, stopping 22 of 23 shots. MacDonald played the third period and the overtime. Jose Theodore went two periods for the Avalanche, saving 16 of 17 shots. Tyler Weitman took over in the final period.