The home team were well on top thanks to three touchdowns from Andre Johnson, but the game seemed to turn when Gary Kubiak had to be taken to hospital after collapsing as he left the field for the interval.
That sapped the atmosphere from the stadium and the players, allowing the Colts to mount a comeback to go 6-2 in the AFC South division.
Case Keenum and Johnson were the stars of the first-half show, as they combined three times - the second being a huge 62-yard throw - to establish 21-3 lead.
Adam Vinatieri brought up the only points on the opening half hour for the Colts, splitting the posts with a 30-yard field goal. He was able to cut the lead to 15 points with another kick early in the third quarter.
Like Keenum and Johnson in the first half, the quarterback found his wide receiver three times to turn the game in favour of the Colts.
The first score came six seconds from the end of the third quarter, but their attempt at a two-point conversion did not come off.
Bullock missed the chance to add three more points to the total and was punished when Luck found Hilton for 58 yards to cut the gap further.
An attempt at a two point conversion was successful after the pair combined once more with four minutes left on the clock, meaning that the Texans trailed by three.
With just seconds left on the clock, Bullock had the chance to force overtime with a kick from 55 yards, but he missed for the third time to see the Texans go 2-6 for their season.