RSL center back Chris Schuler's giveaway in front of the RSL goal gave Brown a chance from the right side, and the forward buried it.
RSL dominated possession for most of the half but could not find the back of the net.
Midfielder Kyle Beckerman sent a blast from outside the box that was tipped away by Rapids' keeper Matt Pickens in the game's third minute. On the ensuing corner kick, RSL defender Kwame Watson-Siriboe collided with Pickens, breaking his right forearm.
Colorado was forced to use backup keeper Clint Irwin, the team's third goalie of the young season.
RSL had chances to test the backup in the first half but couldn't get a shot on frame.
Forward Robbie Findley did well to get behind Colorado's defensive four, but his touch failed him in his first action back at Rio Tinto Stadium. In the 18th minute, Findley chipped a chance in front of the goal well over the crossbar and into the stands.