Houston is now 0-12 all time when playing the Colts in Indianapolis.
The only offensive highlight for the Texans came in the first quarter when Reggie Bullock kicked a 49 yard field goal. The Texans trailed the Colts 7-3.
The Texans failed to get in the end zone, as starting quarterback Case Keenum struggled all afternoon with two interceptions and no touchdowns.
Keenum fumbled in the end zone in the third quarter when left tackle Duane Brown recovered the ball for a safety.
"My teammates deserve better, my coaches deserve better. Our fans deserve better," said Keenum.
Luck opened up the offense even more with a quick shovel pass to running back Trent Richardson for the 9 yard touchdown run, for the 17-3 score in the second quarter.
Adam Vinatieri made a 43 yard field goal after Butler's interception that increased the lead 20-3.
"We definitely needed it," coach Chuck Pagano said. "We talked all week about coming back and even though we had clinched the division, we wanted to start building or gaining some momentum."
The Colts are still an excellent position to make the playoff and win the AFC South.
Texans quarterback Case Keenum finished 18/34 for 168 yards in the loss. Andre Johnson only caught four passes for just 18 yards on the afternoon.
Colts quarterback Andrew Luck finished 19/32 for 180 yards, and one interception that he forced in double coverage in the end zone.
"We played good football today, kept the mistakes to a minimum and were just able to get after it," Robert Mathis said.
Nothing went right for the Texans, even when they decided to go in a new direction with the firing of Gary Kubiak, and defensive coordinator Wade Phillips was promoted as interim coach.
"I thought we could compete with them, but we didn't do a good job of that, " said Phillips. "We looked like a team that lost 11 in a row playing a good football team."
The Texans running game continues to excel despite the losses, with Ben Tate rushed for 72 yards on 16 carries.
The Texans face a tough test back at Reliant Stadium next Sunday, when they face Peyton Manning and the Denver Broncos.