Ballard hauled in a Luck's screen pass and dove headfirst over the pylon in the corner of the end zone. The play had to be reviewed by the officials before he was awarded the game-winning score.
The big play was set up when Luck hit Reggie Wayne over the middle for 20 yards to the Titans 16-yard line on 3rd-and-8.
Luck went 26-of-38 through the air for 297 yards, one touchdown and one interception for the Colts (4-3), who snapped a 10-game road losing streak.
Donald Brown compiled 80 yards on 14 carries and Ballard finished with 55 yards on 12 carries for Indianapolis.
Matt Hasselbeck completed 22-of-29 passes for 236 yards and a TD pass for the Titans (3-5).
Chris Johnson ran for 99 yards on 21 carries.
Texas principal bans speaking Spanish, stirs controversy
Man spent 15 hours in jail for plugging electric car into an outlet at a school