Colorado won, 4-2, thanks to saves by goalkeeper Preston Burpo on shots by Chris Klein and Mike Magee.
Saturday's embarrassment had turned away the remaining Galaxy faithful, and the rematch was played in a near-empty Home Depot Center.
The Rapids' Greg Dalby received a red card in the 36th minute, but the Galaxy failed to score, putting only six of its 24 shots on target.
Galaxy star Landon Donovan, coming off two World Cup qualifiers and an MLS game in the space of a week, watched the game from the stands.
The game marked the Galaxy debut of former U.S. national team defender Gregg Berhalter.
The Rapids will play either the Seattle Sounders FC or Real Salt Lake in the second MLS qualifying round. Seattle and RSL meet April 28.