Tebow's score came with just over 3 minutes to play in the game and completed a comeback from a 17-point deficit for the Broncos (4-11).
Tebow went 16-of-29 through the air for 308 yards, a touchdown and an interception in his second career start. His yardage total was the most for a Denver rookie quarterback in a game since John Elway tossed for 345 yards against Baltimore in 1983.
Brandon Lloyd made five catches for 111 yards and Correll Buckhalter scored both rushing and receiving touchdowns for the victors.
The Texans (5-10) got 310 passing yards and TD from Matt Schaub and Arian Foster chipped in with 91 yards and a score on 19 rushes.