Cale Makar scored two goals and Alexandar Georgiev made 24 saves for the Avalanche, who now trail the Stars 3-2 in the series.
Joe Pavelski opened the scoring with a backhand shot from the doorstep at 9:03 of the first period.
Artturi Lehkonen tied the game with his sixth goal of the playoffs on the power play with a one-timer from the slot at 19:59 of the first period.