That put even more pressure on Alex Smith, who was 30 of 46 for 378 yards with four TDs and no interceptions but lost a fumble that led to a touchdown for Indy. Just about everyone other than the Colts figured Smith sealed the win with a 10-yard TD pass to Davis less than two minutes into the third quarter.
Instead, he tried to rally the Chiefs after Hilton's score and wound up throwing to Dwayne Bowe -- who caught the ball but was out of bounds -- on fourth-and-11 with 1:55 to play from the Indy 43.
"Anytime you're leading like that and then have them battle back and then take it, and you end up losing by a point, it's tough, a tough pill to swallow," Smith said.
Things appeared bleak with Indy trailing 31-10 at halftime, and they got worse when Luck's first pass of the second half was picked off and returned to the Indy 18. Three plays later, Smith made it 38-10.
But Luck had plenty of time to make the jaw-dropping rally.
With Indy going no-huddle, Luck started throwing at will. He eventually caught the Chiefs defense off-guard when Donald Brown scored on a 10-yard run to start the rally. Then Luck capitalized on the fumble by hooking up with Brown on a 3-yard TD pass to make it 38-24.
After Luck's third interception turned into a 42-yard field goal, he answered with a 12-yard TD pass to cut the deficit to 41-31 after three quarters.
The Chiefs only pressured Luck on 2-of-25 dropbacks, according to ESPN Stats & Information. They also allowed him to complete 8 of 9 passes on throw of 10 or more yards.
"He's as advertised. He went out there and definitely avoided some pressure and made big plays down the field," Chiefs cornerback Sean Smith said, referring to Luck.
Even when Eric Berry jarred the ball loose from Brown near the goal line, Luck had the answer. He scooped up the bouncing ball and squirted through the middle to make it 41-38. And after a Kansas City field, goal, Luck found Hilton to win it.
"It seemed surreal, being down like we were down and then you have that fourth-down stop and they had used their last timeout there at the 2-minute warning," Pagano said. "Thinking about how good tomorrow's going to be, snow or no snow, I don't really care."
The Chiefs rushed for 150 yards on 32 carries, even with Charles out most of the game. ... Colts K Adam Vinatieri became the first player in NFL history to score 200 points in the playoffs. He now has 205. ... Indy won its first playoff game without Manning since Jan. 7, 1996, when Jim Harbaugh was the QB. ... The Chiefs fell to 0-4 vs. Colts in playoff matchups.
Information from The Associated Press was used in this report.