The loss, plus Denver's win over Houston, means Kansas City takes the fifth seed in the AFC playoffs as the Broncos win the AFC West title.
After the defense forced a three-and-out on Indianapolis' first possession, Jamaal Charles picked up where he left off in a five-touchdown performance at Oakland. The running back broke through for a 31-yard touchdown run on the fifth play from scrimmage, putting Kansas City (11-4) on top 7-0.
The offense couldn't capture that same efficiency for the rest of the afternoon. Alex Smith and rookie running back each fumled twice, while Smith threw two interceptions after throwing just six in the Chiefs' first 14 games. The Colts capitalized with 14 points off turnovers.
Smith went 16 for 29 for 153 yards and zero touchdowns.
Donald Brown scored both Indianapolis touchdowns, the first on a 33-yard pass from Andrew Luck in the second quarter, putting Kansas City in a 10-3 hole.
Brown took off for a 51-yard scoring run early in the third quarter to put the Colts (10-5) up 20-7.
Adam Vinatieri booted three field goals, while he and Ryan Succop both missed on one attempt.