Both teams exchanged several punts to start the game, before the Texans took a 10-play, 82-yard drive into the end zone for an early 7-0 lead.
The Colts fired back with a pair of unanswered touchdowns in the second. The first score was a 4-yard Marlon Mack run, followed by a Andrew Luck's 14-yard pass to Eric Ebron.
Adam Vinateri closed out the first half with a 54-yard field goal to make it 17-7.
In the second half, Lamar Miller struck first on a 1-yard touchdown run to bring Houston within three points.
Unfortunately, Luck hit Zach Pascal for his second touchdown of the game to go up 24-17.
A DeAndre Hopkins touchdown catch with 2:37 left in the game gave the Texans one last bit of hope for a comeback, but on the ensuing Colts possession, a neutral zone infraction penalty by Jadeveon Clowney sealed the Colts victory.
While the loss ends the Texans 9-game winning streak, the team still controls its own destiny.
Three games remain on the season and the Texans still hold a two game lead over the Tennessee Titans and Colts to clinch the AFC South.
In addition, with the New England Patriots loss to the Miami Dolphins, the Texans still have a chance at securing a first round bye week.