Sproles' winning run came 8:48 left in the extra period. The victory gave the Chargers a 9-8 record, and ended the Colts' nine-game winning streak.
Sproles, who got extended playing time because of an injury to LaDainian Tomlinson, scored twice and compiled 328 all-purpose yards -- 105 rushing, 45 receiving and 178 combined return yardage.
Phillip Rivers completed 20-of-36 passes for 217 yards with one interception, and Tomlinson rushed for one touchdown while gaining just 25 yards on five carries before leaving in the second quarter.
Antonio Gates caught eight passes for 87 yards for the Chargers.
San Diego, the 12th club ever to qualify for the post-season with an 8-8 record, will play either the Tennessee Titans or AFC North champion Pittsburgh next week.
Peyton Manning -- who this week won his third NFL NVP Award -- was 25-of-42 passing for 310 yards and a touchdown. Joseph Addai ran for a TD and Adam Vinatieri kicked a 43-yard second-quarter field goal for the Colts, who had beaten the Chargers 23-20 Nov. 23.
Manning reached the 4,000-yard plateau in his NFL playoff appearances -- getting ther faster than any other quarterback.