The Texans have won a combined 11 games over the past three years under three head coaches, not counting the interim coach. They have 10 wins this season, their first playoff berth since 2019.
Houston beat Indianapolis 23-19 in a win-or-go-home game on Saturday night.
The Texans (10-7) can win the AFC South if the Giants upset the Jaguars on Sunday. The Colts fell to 9-8.
C.J. Stroud, the leading candidate for Offensive Rookie of the Year, threw two touchdown passes and had a crucial drive in the fourth quarter to lead the Texans to victory. He went 20 of 26 for 264 yards.
He threw a 75-yard touchdown to Nico Collins on the team's first snap and a 1-yard touchdown to Andrew Beck in the final two minutes of the first half.
Collins caught nine passes for 195 yards, while six other players caught 11 passes for 69 yards. The Texans were missing their key third, fourth and fifth receivers.
Stroud led the Texans on a 12-play, 73-yard drive, and Devin Singletary scored on a 3-yard run with 6:20 remaining. They overcame a 22nd-place finish after a Stroud sack by Ronnie Harrison Jr. and a 21st-place finish after a penalty on Beck.
Kicker Kaimi Fairbairn missed the extra point wide left, putting the Texans' defense on the spot.
The Colts got to the Houston 15 with 1:06 remaining and faced fourth-and-1. Instead of running Jonathan Taylor, who had 30 carries for 188 yards and a touchdown, Shane Steichen opted to put the ball in Gardner Minshew's hands. Running back Tyler Goodson was open but the throw was a little behind him and he dropped it.
The Texans ran three and got a safety on the punt, leaving one second on the clock. The Colts picked up just 7 yards on the free kick before Houston recovered Michael Pittman's lateral attempt.
Taylor left briefly at the end of the third quarter due to heel and ankle injuries, but returned. It kept the Colts in the game, as Minshew struggled going 13 of 24 for 141 yards.
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