The Colts had just taken a lead on Adam Vinatieri's 37-yard field goal with 56 seconds left, but the Jaguars (1-2) came right back.
On the decisive play, Gabbert hit Shorts with a pass, and he ran past the Colts defense into the end zone for a touchdown, followed by an unsuccessful 2-point conversion attempt with 45 seconds remaining.
The Colts (1-2) then staged a last-chance drive, and Andrew Luck got Indianapolis to the Jacksonville 26 with a 36-yard strike to T.Y. Hilton.
But on the last play of game his pass into the end zone was batted away.
Notable deaths of 2014 [PHOTOS]
Michael Sam cut from the Dallas Cowboys