INDIANAPOLIS — The Indianapolis Colts had all the Luck — at least once the second half started.Andrew Luck threw three touchdown passes after halftime, including a 64-yarder to a wide-open T.Y. Hilton for the go-ahead score with 4:22 left, leading the Colts from a four-TD deficit to an improbable 45-44 comeback victory over the Kansas City Chiefs in a wild-card game Saturday.Indianapolis (12-5) became only the second team in playoff history to win after trailing by 28 or more points, according to STATS. The other: Buffalo over Houston 41-38 in overtime in January 1993. The Colts will travel to either Denver or New England next weekend for the divisional round.Luck was an incredible mix of good and bad, finishing 29 of 45 for 443 yards, the second-highest total in franchise history for a playoff game, with four TDs and three interceptions. He also picked up a fumble and ran it in for a 5-yard score when the loose ball bounced back to him.Hilton broke a franchise playoff record with 13 catches and 224 yards, finishing with two TDs — including the winner.Kansas City (11-6) finished its turnaround season with three straight losses, two to the Colts and an eighth straight postseason defeat, breaking a tie with the Detroit Lions for the longest playoff skid.Alex Smith was 30 of 46 for 378 yards with four TDs and no interceptions on a day he lost his top two running backs, Jamaal Charles and Knile Davis, and starting receiver Donnie Avery to injuries.But Luck got the last word with his jaw-dropping rally.Things appeared bleak with Indy trailing 31-10 at halftime, and they looked even worse when Luck’s first pass of the second half was picked off and returned to the Indy 18. Three plays later, Smith threw a 10-yard TD pass to Davis to make it 38-10 with 13:39 left in the third quarter.