Luck overcame three interceptions to throw for 443 yards with four touchdowns -- including a go-ahead, 64-yard TD pass to T.Y. Hilton with 4:29 remaining -- as the Colts overcame a late 28-point deficit with one of the biggest comebacks in NFL post-season history.
Luck also scored on the recovery of a Donald Brown fumble at the Kansas City 2-yard line midway through the fourth quarter, drawing the Colts to within 41-38.
The Chiefs then rallied with the second of Ryan Succop's second-half field goals at the 5:40 mark. But on the next drive, Luck (29-of-45 passing) threw a bomb to Hilton, who split the defense for a long score and the Colts' first lead of the game.
Quarterback Alex Smith couldn't rally the Chiefs on their last-gasp drive, sending the fourth-seeded Colts into the AFC semifinals.
Hilton ended with 13 catches for 224 yards -- third-most ever in a playoff game -- and two touchdowns, helping Indianapolis outscore Kansas City 35-6 down the stretch.
Smith completed 30-of-46 passes for 378 yards, four touchdowns and no interceptions for the Chiefs, who played nearly all the game without star running back Jamaal Charles (concussion).
Kansas City fell to 0-8 in its last eight playoff games.
2014: The Year in Music [PHOTOS]