The Colts faced a 20-17 deficit when Manning's 17-yarder to the running back with 3:10 left put them in front for good. The win was secured when cornerback Melvin Bullitt intercepted Ben Roethlisberger's desperate heave into the end zone on the game's final play.
Overall, Manning tossed three touchdown passes, finishing 21-of-40 passing for 240 yards.
Reggie Wayne and Dallas Clark also caught scoring passes, with Wayne making a team-high six receptions for 114 yards for the Colts (5-4), who needed a win after AFC South-leading Tennessee grabbed a 21-14 win over Chicago earlier.
Roethlisberger went 30-of-42 for 284 yards with no touchdowns and three interceptions.
Running back Mewelde Moore scored twice, while Jeff Reed kicked two field goals for the Steelers (6-3), who fell into a tie with Baltimore atop the AFC North.