The Jaguars offense managed to rack up 431 yards against the Colts, but couldn't convert all that offense into the points to match and missed a pair of game-winning field goal attempts from Jason Myers.
The second missed attempt at a game-winner set up the Colts with good field position in overtime, and a 53-yard drive quickly followed to set up Adam Vinatieri for a chip shot winner.
Hasselbeck, 40, had to take over for Luck and wasn't able to lead the Colts to many points in a game that featured 14 combined punts between Pat McAfee and Bryan Anger.
For Jacksonville, it was another example of a strong start being spoiled by momentum coming to a grinding halt in the second half. A game-winning field goal against the Miami Dolphins in Week 2 temporarily made up for that problem, but when Myers missed two chances in Week 4, the Colts took advantage.
It is the 15th consecutive divisional win for the Colts, who improve to 2-2 after back-to-back wins and have a Thursday night game against the Houston Texans up next. The Jaguars, who seem perennially adept at snatching defeat from the jaws of victory, will look to get back on track in a road game against the Tampa Bay Buccaneers.