Lewis' fourth goal of the season sealed the win for the Rapids, who have lost just once in the past six games. Colorado vaulted into sixth place and a postseason position in the MLS Western Conference.
The Galaxy played with 10 men from the 75th minute on after Julian Araujo was shown a red card. Araujo drew a yellow card for a foul in the 72nd minute, then was given red for his reaction to the call.
The Galaxy saw its streak of six matches without a loss came to an end.
Bassett's 40th-minute goal gave Colorado a 1-0 lead. Bassett scored off a long cross from fullback Sam Vines, who had no one marking him on the left wing as he dribbled and looked for someone in the box.
The ball found Bassett's feet, and his shot was too forceful for David Bingham to stop for the Galaxy.
Joe Corona got an open look from outside the top of the box in the 42nd minute for the Galaxy, but William Yarbrough stopped it for the Rapids. Yarbrough finished with four saves.
The Galaxy chose not to start a pair of stars, forward Javier "Chicharito" Hernandez and midfielder Jonathan dos Santos, but both came on as substitutes in the 54th minute. Just before that, Yarbrough stopped Ethan Zubak's redirected cross from in front of the net to keep the Galaxy scoreless.
Bingham came up big for the Galaxy in the 65th minute. After a shot from Lewis hit the goal bar, the rebound remained with the Rapids. Andre Shinyashiki had a chance from close range, only to have Bingham turn him away.
The Galaxy fell to eighth place in the West.