Playing in his first game since breaking his left forearm last month, Baudet was standing in front of an open net when he received a corner kick from Mehdi Ballouchy and buried a header past goalkeeper Pat Onstad.
Goalkeeper Matt Pickens posted his sixth shutout of the season and 17th of his career for Colorado (9-7-6).
Houston (11-7-7) extended its winless skid to three. The Dynamo have a two-point lead over Los Angeles in the Western Conference.
Scoring chances were at a premium in the first half. A shot by Houston's Stuart Holden barely missed the right post two minutes into the game. Moments later, Colorado's Nick LaBrocca sent a weak header into Onstad's stomach.
Onstad easily caught Jacob Peterson's shot from 25 yards in the 24th minute and came out of the crease to take the ball off Omar Cummings' right foot in the 41st.
Play opened up briefly at the start of the second half. Pickens came out to stop Kei Kamara on a breakaway in the 49th minute. Seconds later, Onstad batted away a shot by Peterson.
Pickens also stopped a shot by Kamara in the 68th minute. A header by Kamara from inside the crease brushed the outside of the right post in stoppage time.
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