Brandon Weeden also put them in the AFC South lead.
With Houston's top two quarterbacks out, Weeden was pressed into service late in the first half Sunday, and the 32-year-old responded by giving the Texans their first win ever on the Colts' home turf.
Weeden led Houston to two field goals before throwing an 8-yard go-ahead touchdown pass to Jaelen Strong with 10:36 left to help Houston rally for a 16-10 victory.
"He's a pro, he acts like a pro, he carries himself like a pro, he is a pro," coach Bill O'Brien said. "Look, I'm not sure he has the whole offense down pat, but I think he has enough that he can go in there and function."
The former first-round draft pick and one-time starter was released after two seasons in Cleveland. Eventually, he signed with Dallas, was benched in October and cut in November. Houston claimed him off waivers Nov. 18 as an insurance policy -- one that paid handsome dividends in an ugly win.
Houston (7-7) won for the first time in three weeks, snapped a six-game skid in the series and improved to 1-13 all-time in Indy.
Thanks to a stifling defense, which allowed just 190 yards, and the resurgence of Weeden, the Texans now have the inside track to their third division crown in five years.
"I've only been here a month, but I found out early in the week that we had never won here and I think guys were hungry," Weeden said. "I think guys kind of knew what we were playing for and all that was at stake."
The question now is how much longer Houston will need Weeden?
Starting quarterback Brian Hoyer missed the game with a concussion. His replacement, T.J. Yates, left with 1:14 to go in the first half because of an injured left knee. He was hurt on a scramble run that was wiped out because of a holding call on Duane Brown.
O'Brien said he didn't expect Yates to play next week and didn't provide a specific update on the injury, though the CBS broadcast said initial reports indicated it was an ACL injury.
Hoyer's status for next week, O'Brien said, remains unclear.
This battle of backup quarterbacks certainly didn't earn many style points.
Weeden finished 11 of 18 with 105 yards, but found Strong on the critical screen play on the right side. Strong caught it, raced up the field and dived into the end zone.
Yates was 6 of 10 with 68 yards and one interception.
The Colts (6-8) weren't in much better shape.
Matt Hasselbeck, who started for the fifth consecutive week as Andrew Luck recovers from a lacerated kidney and partially torn abdominal muscle, was 17 of 30 with 147 yards, one touchdown and one interception.
He couldn't generate any offense in the second half and left briefly in the fourth quarter with what the team called a back injury. Hasselbeck said later that he hurt his jaw.
Indy lost its third straight after Hasselbeck misread a deep route from Donte Moncrief and threw an interception on the first play of the Colts' final series.
"It was just a tough, tough day," Hasselbeck said. "I'm disappointed because we had a chance. We had many chances and we didn't take advantage of them."
The Texans wouldn't allow it.
Houston had two turnovers and terrible field position in the first half, but all the Colts managed was an 11-yard TD pass from Hasselbeck to Moncrief and a 29-yard field goal from Adam Vinatieri for a 10-0 lead.
The Texans got a 22-yard field goal from Novak on the final play of the half, a 46-yard field goal late in the third quarter and the TD pass from Weeden to Strong early in the fourth to make it 13-10. Novak's late 32-yard field goal closed it out.
"We knew when we were 2-5 that we had a good team and we could turn this around," receiver DeAndre Hopkins said. "The Colts kept us in this division by losing a couple of games and we knew that we had to take advantage of it. That's what we did."
Texans receiver Cecil Shorts III left early with a groin injury and isn't expected to play next week. ... Vinatieri played in his 304th career game, breaking a tie with Jerry Rice for No. 6 on the NFL's career list for games played. ... Houston's Alfred Blue ran 20 times for 107 yards. ... Hasselbeck tied Terry Bradshaw and Y.A. Tittle for No. 30 all-time in TD passes (212), and Colts receiver Andre Johnson passed James Lofton for No. 9 in yards receiving (14,015).
AP NFL website: www.pro32.ap.org and www.twitter.com/AP-NFL
Indianapolis Colts QB Carson Wentz has sprains to both his ankles, Frank Reich says
Colts QB Carson Wentz has sprains to both his ankles and his status for Sunday's game against the Titans is unclear, coach Frank Reich said Monday.
Arians confirms Bucs have reached out to Richard Sherman
Bruce Arians addresses his team's interest in veteran cornerback Richard Sherman.
Buffalo Bills fans could end up in Amazon commercial
Casting Buffalo placed an advertisement on Facebook looking for actors to play a role in a new Amazon commercial. Those roles: Bills fans of all kinds.
Sam Acho's 'Macho Men' of Week 2
Sam Acho channels his inner Macho Man to dole out some awards for Week 2 in the NFL.
Fantasy football waiver wire for NFL Week 3: Tony Pollard, Derek Carr among top pickups
Field Yates lists the names you need to know as you seek replacements for injured players or simply try to improve your team following Week 2 action.
Bruce Arians: Tampa Bay Buccaneers have reached out to CB Richard Sherman
Buccaneers coach Bruce Arians said Monday that GM Jason Licht has reached out to cornerback Richard Sherman to gauge his interest in playing for Tampa Bay.