The goals came in a 17-minute span.
Casey scored in the 26th minute, Clark in the 34th, and Petke in the 43rd, as the Rapids (7-9-6) got their third win in a row.
Colorado dominated the first half, playing in front of a sold-out crowd of 18,086, and controlling the ball on both sides of the field for the full 45 minutes.
The Galaxy played without David Beckham, whose injured left ankle has not responded to treatment.
Los Angeles (3-10-5) remained winless on the road, and has dropped its last five games.
Los Angeles is home to Real Salt Lake Saturday, and Colorado travels to Columbus next Sunday.