Eriksson eluded Jan Hejda behind the Colorado goal and attempted a pass to Jamie Benn, but the puck hit Hejda's fallen Avalanche team mate Erik Johnson in front of the net and deflected past goalie Semyon Varlamov for the winner.
"He (Eriksson) quietly goes about his business. I thought he was our best player tonight," rookie Stars coach Glen Gulutzan told reporters. "He just gets things done. He's quietly competitive and he's a good player."
Both teams squandered two-goal leads in the roller-coaster contest and the score was tied on four occasions.
"It was just one of those nights you don't like as a coach but if you came to the game, you feel like you got your money's worth," Gulutzan said.
Matt Duchene had a hat-trick to lead the Avalanche offense, his third goal giving Colorado a 6-5 lead near the mid-point of the third period.
"Matty had his legs moving tonight," Colorado coach Joe Sacco said. "That was key for him. He was skating. He was working hard and that's why he got good results."
Benn, who had a four-point night, tied the game with four minutes remaining and then assisted on Eriksson's winner.
Colorado built a 2-0 first-period lead, but penalty trouble in the second allowed the Stars to score four unanswered goals, three of them on the powerplay.
Duchene and Paul Stastny rallied the Avalanche before the end of the second to send the game into the third tied at 4-4.
Daniel Winnik's rebound goal early in the third period pushed the Avalanche back into the lead before Eric Nystrom scored the Stars' fourth powerplay goal four minutes later.
(Reporting by Mike Mouat in Windsor, Ontario; Editing by John O'Brien)