The defeat in the "win-and-in" clash ended the Colts' hopes of reaching the post-season while Houston could yet win the AFC South division title if Jacksonville lose to Tennessee on Sunday.
Stroud, the number two overall pick in last April's draft, kept his cool in the biggest game of his professional career completing 20 of 26 passes and throwing for two touchdowns and 264 yards with no interceptions.
Stroud becomes just the fifth rookie quarterback in NFL history to reach 4,000 passing yards. He and first-year coach DeMeco Ryans are the first rookie quarterback and coach pairing to reach the post-season since 2012.
It was close down the stretch though, with the Colts' final drive arriving at the Houston 15-yard line with 1:03 left. On fourth and one, quarterback Gardner Minshew's pass short left to Tyler Goodson was dropped.
The Texans led 14-6 at the break after Stroud hurled a 75-yard touchdown pass deep to Nico Collins in the first quarter and then found Andrew Beck with a one-yard pass late in the second.
The Colts levelled the game when Jonathan Taylor broke free for a 49-yard rushing touchdown.
After an exchange of field goals left the game at 17-17, Devin Singletary got the game-winning touchdown with a clever, weaving, three-yard rush with 6:20 left -- but the Texans missed the extra point to leave the door open.
The Colts had been effective with their running game but opted to pass on the crucial fourth and one play and Goodson's drop, with the ball thrown slightly behind him, ended their hopes.
"I think tonight we showed the world what the Texans can do and we're going to continue to do that," said Stroud.
"I put my blood, sweat and tears into this and it's just really cool to see the fruits of your labour come out, I'm super blessed," he added.
The Pittsburgh Steelers kept their playoff hopes alive with a 17-10 win over a Baltimore Ravens team resting their star quarterback Lamar Jackson.
The Ravens secured top seed in the AFC playoffs last week and handed back-up Tyler Huntley a rare start as they opted to protect MVP frontrunner Jackson.
The win for Pittsburgh (10-7) means that they can make it into the post-season with some help from other teams in Sunday's games.
The Steelers will advance if Buffalo lose at Miami or Jacksonville lose or tie their game at Tennessee.
Heavy rain in Baltimore made for tricky handling conditions and both teams adapted with the Steelers quarterback Mason Rudolph making ample use of running back Najee Harris.
Harris, who put up 112 yards on 26 carries, put the Steelers ahead in the first quarter with a powerful six-yard rush at the end of a 12-play, 76-yard drive.
Quite the view
The Ravens (13-4), who also rested some other key starters including wide-receiver Odell Beckham Jr, responded in the second quarter with Huntley finding tight-end Isaiah Likely who bustled past two defenders for a 27-yard touchdown.
Rudolph abandoned his cautious approach on the first play in the fourth to zip a pinpoint pass to Diontae Johnson who collected and ran home for a career-high 71-yard score.
A field goal from Chris Boswell with just over three minutes left put Pittsburgh 10 points up and the Ravens could only manage a field goal from Justin Tucker in response.
"Diontae is a great playmaker and he split them right there and it was quite the view from behind (seeing them) chasing down the field," said Rudolph.
"I'm proud of our guys, we got the big win on the road and hopefully we get some help (on Sunday) and get into the tournament," he added.
The win means that the Steelers reached 10 wins in a season for the 10th straight year under head coach Mike Tomlin.
There was some concern for the Steelers though with top linebacker T.J. Watt, who leads the NFL with 19 sacks, going off with a knee injury.
Both ESPN and the NFL Network reported that Watt had suffered an MCL ligament sprain, raising doubts over his involvement in the wildcard round of the playoffs, should Pittsburgh make it in.
"Obviously disappointed,” Tomlin said of the injury, "but there are challenges in the game of football, challenges in the game of life. So we’ll deal with it whatever it may be."
Follow the final round of the NFL's regular season on Flashscore.
