Marek Svatos scored the winning goal 1:24 into the third period. Milan Hejduk added a goal and an assist, and Joe Sakic had two assists. Calgary and Colorado faced each other for the third time in six days. The teams split two games in Calgary last week. Miikka Kiprusoff had 28 saves.
Budaj has given up 16 goals in his last four starts against the Flames, but was at his best early in the third period when Calgary had a five-on-three advantage. He even took a point-blank shot square in the mask.
Stastny's two power-play tallies in the first period gave him 21st goals this season.
Kristian Huselius had a goal and an assist, raising his season total to five goals and five assists against the Avalanche.
Stastny has 53 points this season, breaking the Avalanche record for the most by a rookie. Former Colorado player Alex Tanguay, who now plays for Calgary, set the mark with 51 in the 1999-00 season.
Stastny's father, Peter, has the franchise record - scoring 109 with Quebec during the 1980-81 season.
The Flames and Avalanche have combined for 43 goals in five games this season.
The Avalanche moved into a fourth-place tie with Edmonton in the Northwest Division. Colorado still trails Minnesota by nine points for the final playoff spot in the Western Conference.