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The Texans were on the scoreboard with 1:51 left in the first quarter as Randy Bullock kicked a 49-yard field goal to reduce the deficit to four points.
Indianapolis restored that lead back to seven early in the second quarter when Adam Vinatieri cancelled out Bullock's kick with a 37-yard effort of his own.
The hosts then moved further ahead midway through the quarter when Luck threw a shovel pass to Trent Richardson, who made his way into the endzone from nine yards.
Vinatieri added another field goal with less than two minutes to go until the halfway stage as the Colts went into the break 17 points to the good.