The Colts entered the match without starting quarterback Andrew Luck, who was ruled out of the contest with a shoulder injury.
The Jaguars got back into the game when Blake Bortles sent the ball long for Allen Robinson, who made a 48-yard reception to take his side to the goalline. However, Jason Myers was forced into action as the visitors failed to find the endzone, but the kicker tied the game at 3-3.
Jacksonville took the lead on their next possession as they turned the ball over from the Colts, and Bortles then drove his side into the redzone before the quarterback found Robinson for an eight-yard touchdown.
Indianapolis responded as they managed to win a string of penalties before Hasselbeck found tight end Coby Fleener in the endzone for a two-yard strike.
The Jaguars retook the lead just before the break when Myers added his second field goal of the game by sending his kick through the posts from 32 yards.