The Colts improved to 15-1 against Houston (5-6).
Manning threw two first-half interceptions, but had a pair of second-half TD passes, including a 4-yarder to Dallas Clark that gave the Colts a 21-20 lead with about nine minutes left.
Clint Session stretched the lead to 28-20 when he returned an interception by Matt Schaub 26 yards for a touchdown seconds later. Schaub fumbled on Houston's next possession and Chad Simpson's touchdown run put the game out of reach.
The Colts can clinch the AFC South title if the Jaguars lose to the 49ers later Sunday. The loss makes Houston's chances of earning its first playoff berth more dim.
Houston, which has lost three straight, was all but unstoppable in the first half, and the Texans scored on their first four possessions. It was a different story after halftime, with the Texans unable to get anything going offensively until Schaub hit Jacoby Jones for a touchdown with 18 seconds remaining.
The Colts' first lead came on Manning's touchdown pass to Clark. In what was a theme Sunday, the drive was helped by a 17-yard pass interference penalty on Houston.
It was the fifth straight week the Colts have trailed in the fourth quarter. Earlier in the period, Indianapolis had a first down at the Houston 13, but the next three plays netted 1 yard to set up a field goal attempt early in the fourth quarter. Matt Stover's 32-yard attempt sailed wide right to keep Houston's lead at 20-14.
In the third quarter, the Texans were called for pass interference on third-and-goal from the 8-yard line, giving the Colts a first down at the 1. Reggie Wayne caught a touchdown pass three plays later to make it 20-14.
Houston's Jacques Reeves got a 43-yard pass interference penalty on the third play of that drive.
Antoine Bethea intercepted Schaub's throw on Houston's next drive, but the Colts couldn't convert.
Manning finished 27 of 35 for 244 yards. Schaub was 31 of 42 for 284 yards with two TDs and two interceptions.
The Colts' first score came when Manning found Pierre Garcon for a 9-yard touchdown about six minutes before halftime. That drive was helped by a 15-yard roughing-the-passer penalty on Antonio Smith for hitting Manning in the head.
The Texans got in red zone on two of their first-half possessions, but came away with field goals after those drives stalled to lead 20-7 at halftime.
The Colts were driving just before halftime and were at their 37 when Manning was picked off for the second time, this interception by rookie Brice McCain.
Houston scored on its first possession for the first time this season when Schaub completed an 11-play, 79-yard drive with a 7-yard pass to Vonta Leach to make it 7-0.
The Texans marched downfield again on the next drive and went up 14-0 on a 5-yard run by Chris Brown. Schaub connected on his first eight passes and didn't throw an incompletion until the second quarter.
Manning was under heavy pressure from Smith and Amobi Okoye when he threw an interception to Brian Cushing early in the second quarter. The Texans got to the Indianapolis 12 before Kris Brown's 35-yard field goal pushed the lead to 17-0.
The Colts were without star defensive end Dwight Freeney, out with an abdomen injury.