With his team trailing 17-10 midway through the third quarter, Josh Freeman led the Buccaneers on a 13-play, 80-yard drive, hitting Preston Parker with a 13-yard scoring strike with 14 seconds left in the period to forge a 17-17 tie.
Blount gained 52 of his 127 yards on the decisive fourth-quarter drive -- including a 35-yard scoring run -- and the Buccaneers (3-1) won their third straight game after opening the season with a loss to Detroit.
Freeman completed 25 of his 39 pass attempts for 287 yards and added a rushing touchdown in the victory.
Curtis Painter, starting his first game under center in place of an injured Kerry Collins, was effective but couldn't produce a win for the Colts (0-4), who remained winless in the absence of Peyton Manning.
Painter threw for 281 yards and two touchdowns but was just 13-for-30 and lost a fumble as Indianapolis logged its worst start since 1998 -- Manning's rookie season.