Joe Pavelski scored the go-ahead goal in the third period for the Stars. Jake Oettinger stopped nine of 10 shots before being replaced at the start of the third by Scott Wedgewood, who made nine saves.
Ondrej Pavel scored, and Justus Annunen made 27 saves for the Avalanche.
Pavel scored a short-handed goal at 2:05 of the second period to give Colorado a 1-0 lead.
Robertson tied it 1-1 at 18:17.
Pavelski put the Stars in front 2-1 with a power-play goal at 13:20 of the third, and Craig Smith scored into an empty net with three seconds left for the 3-1 final.
