The Colts climbed to 6-3 and stayed in position to grab one of the AFC's two wild-card playoff berths one year after winning only two games all season.
Indianapolis trails Houston by 1 1/2 games for the lead in the AFC South. The Colts and Texans will meet twice during the final three weeks of the season.
The Jaguars lost their sixth in a row and dropped to 1-8. They continue to play without running back Maurice Jones-Drew, who gained 1,606 yards last year but has now missed three games in 2012 with an injury.
Luck, the first player chosen in this year's draft, completed 18-of-26 passes with one interception.
He drove the Colts 66 and 61 yards to second-period touchdowns and he scored on short runs at the end of both those marches.
That gave Indianapolis a 17-0 lead and the Colts' other touchdown came on an 11-yard interception return by Darius Butler early in the third period. Adam Vinatieri kicked two field goals to open and close the Indianapolis scoring.
Jacksonville changed quarterbacks during the game after Blaine Gabbertt had completed 18-of-31 passes for 209 yards and had thrown the interception that was brought back for a score.
Chad Henne came on to throw a 4-yard, fourth-quarter touchdown pass to Cecil Shorts at the end of an 81-yard drive.