Even interim coach Bruce Arians had been dancing.

“It’s a fun locker room, a great locker room,” Luck said after leading Indianapolis to a 20-13 victory over Kansas City. “You know guys are going to play hard no matter what the score, no matter what the situation, and I am very proud to be a part of a team like that.”

A team that’s headed back to the playoffs, too.

Luck threw for 205 yards on Sunday, breaking Cam Newton’s single-season mark for yards by a first-year quarterback. He also engineered the go-ahead drive late in the fourth quarter, hitting Reggie Wayne on third-and-goal from the Kansas City 7 with just over 4 minutes remaining.

The touchdown pass finished off Luck’s seventh four-quarter comeback this season, and allowed the Colts (10-5) to join the Miami Dolphins of 2008 as the only teams in NFL history to win at least 10 games one year after losing 14 or more.

“Would we have done it without him?” Arians asked. “No.”

Luck broke Newton’s record of 4,051 yards passing in the second quarter, and then became the fifth rookie quarterback in the Super Bowl era to win at least 10 games in a season.

“Obviously it’s nicer to be in the playoffs,” Luck said, “but it’s nice to have a couple records — which I’m sure will be broken in the next year.”

Don’t be quite so sure.

Luck still has next Sunday’s game against Houston to pile up numbers, and then comes a trip to the playoffs, where the Colts became a mainstay under his predecessor, Peyton Manning.

“We didn’t want to slide in the backdoor and put the extra stress on a man having to win the next game,” Luck said. “So we are very glad to be going to the postseason.”

Arians will also get a reprieve from shouldering so much of the burden. Colts coach Chuck Pagano, who has undergoing treatment for leukemia, plans to rejoin the team this week.

Jamaal Charles ran for 226 yards for the Chiefs, including an 84-yard scamper on the first play of the second half as his team rallied to forge a 13-all tie entering the fourth quarter.

It was Charles’ second 200-yard game of the season, and the third of his career, and came one week after he managed 10 yards on nine carries against Oakland.

“It was fun today, competing out there and doing it while we were trying to come back,” Charles said. “It was fun going out there and putting out a performance like that.”

Charles joined the Titans’ Chris Johnson and former Lions great Barry Sanders as the only players with three runs of 80 or more yards in a season.

Peyton Hillis added 101 yards on the ground for the Chiefs (2-13), who finished with 352 yards rushing in a losing effort. A big reason why was Brady Quinn, who was just 10 of 22 for 162 yards with two interceptions through the air.

“This game was without a doubt, 100 percent on my shoulders,” Quinn said. “You can’t play the way I played today and win a football game.”

His trouble began with the Chiefs’ fifth offensive play, when he threw woefully behind Dexter McCluster — who wasn’t even looking for the ball. Darius Butler picked off the pass in stride, and took it untouched 32 yards to give the Colts a 7-0 lead.

Kansas City managed a field goal by Ryan Succop, but he missed his next try and the Colts went the other direction to set up the first of Adam Vinatieri’s two field goals.

Charles fumbled in the red zone later in the second quarter, and the Colts moved into Vinatieri’s range for a 36-yard field goal and a 13-3 halftime lead.

Charles electrified a sparse crowd on the first play of the second half. He angled to the left and then found room down the sideline, cutting back toward the middle of the field and winning a foot-race with the Indianapolis defense for an 86-yard touchdown run.

The Chiefs were in position to take the lead later in the third quarter, but Quinn was picked off by Vontae Davis in the end zone. The defense forced a three-and-out and Kansas City was driving again before settling for Succop’s tying 47-yard field goal.

The Chiefs got the ball back again late in the fourth quarter, but Quinn was stuffed on a quarterback sneak on fourth-and-inches from the Indianapolis 27.

That turned the ball over to Luck, who completed an 11-yard pass to T.Y. Hilton to convert a third down before he and Wayne won it.

“At times it looked a little bleak,” Arians said. “Guys hung in there, made plays when they had to make them. Offensively we struggled, and then put together a drive, like we have all year.”

NOTES: Chiefs WR Terrance Copper (left knee) and DT Tyson Jackson (left foot) left with injuries. … Wayne had five catches to become the fifth player in NFL history with four 100-catch seasons. He also became the 14th player to reach 13,000 yards receiving.