Luck finished 22-of-36 through the air with an interception as the Colts (3-1) overcame a slow start to run off the game's final 37 points.
Trent Richardson scored on a 1-yard run in the second quarter and Darius Butler returned an interception for a score in the victory.
Blaine Gabbert was picked off three times and limited to 179 aerial yards on 17-of-32 efficiency for the reeling Jaguars (0-4), who opened a season with fourth straight loss for the first time since 2003.
Newt Gingrich fires back at Mandela backlash
Wisconsin business offering 'therapeutic cuddling' forced to close