It was the Rapids' first win on Dallas' home turf in seven years.
Colorado jumped from last place in the Western Conference into a third-place tie with Chivas USA going into this weekend's action. It was Colorado's first road win since a 1-0 victory over New England April 12.
Petke's goal came in the 60th minute when he converted a header to the near post off a corner kick from Terry Cooke.
Dallas missed a chance to tie it in the 80th minute when Drew Moor's header failed to find a wide-open goal.
Dallas leads only San Jose and Los Angeles in the Western Conference. Those teams are just a point behind Dallas with a game in hand.