Manning hit Jacob Tamme with a 2-yard scoring pass in the first quarter for the game's initial score and the Colts (5-2) never relinquished the lead.
Kelvin Hayden returned an interception 25 yards for a touchdown and Vinatieri connected on the first of his field goals with 53 seconds left in the half, putting Indianapolis up 17-3 at the break.
Manning completed 26-of-45 passes for 268 yards with no interceptions and Mike Hart racked up 84 yards on 12 carries for the Colts, who won their third straight and downed the Texans for the 16th time in 18 all-time meetings.
Houston (4-3) was led by Matt Schaub, who connected on 22-of-38 pass attempts for 201 yards with one touchdown and one costly interception.
Arian Foster picked up 102 yards rushing on 15 carries for the Texans.