Budaj was especially tough in the second period when the Stars launched 14 shots en route to his first shutout of the season and ninth of his career.
Colorado got a pair of goals in the middle frame to put the game away -- one from Milan Hejduk and a short-hander by Phillippe Dupuis for a 3-0 lead.
Dupuis added a pair of assists and Brandon Yip also scored for the Avs, who won for the third time in four games.
Dallas goalie Andrew Raycroft was lit up for five goals on 45 shots.
Notable deaths of 2014 [PHOTOS]