Dillon Powers added a goal and an assist for Colorado (9-7-7). The Rapids beat the Galaxy for the first time in seven meetings and had been 0-5-1 over that span.
Colorado is unbeaten, 4-0-2 in its last six games after going through a 0-4-1 stretch.
Thomas found space between two defenders when Powers lined up for a corner kick. Powers put the ball right on the head of Thomas, whose header sailed past goalkeeper Carlo Cudicini.
Los Angeles (10-9-3) was looking for its fifth win in seven matches. The Galaxy was shut out for the sixth time this season in falling to 1-6-0 in its last seven road games.
Colorado added a goal in the 47th minute when Edson Buddle found Powers in stride just over the midfield stripe. Cudicini came out to stop the shot, but Powers got the ball under the lunge of Cudicini.
The Galaxy was without Landon Donovan and Robbie Keane. Donovan missed his fifth straight game due to service with the U.S. national team while Keane sat out with a left hip flexor strain suffered the previous weekend.
Hector Jimenez found an opening in the 15th minute, but fired a shot over the crossbar for the Galaxy. Juninho barely missed with a shot from 30 yards in the 22nd minute. His shot grazed the left post.
Colorado's Clint Irwin caught a shot from the left wing by Galaxy's Todd Dunivant at the close of the half in added time.
Referee Juan Guzman issued three yellow cards in the first half.
Thomas drew a yellow card for upending Juninho in the ninth minute. Thomas will serve his second suspension of the season when the team plays Aug. 3 against Real Salt Lake.
The Galaxy's Juninho and Pablo Mastroeni, a former Colorado midfielder, received theirs moments apart after disputing non-calls. Juninho had been hauled down by Shane O'Neill in the 30th minute.
The Galaxy didn't test Colorado goalkeeper Clint Irwin. Irwin produced his eighth shutout of the season.