Being the heir to Peyton Manning in Indianapolis is heady stuff for a rookie taking the reins of a franchise that won two games last season.

Now, after guiding the Colts back to the playoffs — and breaking Cam Newton’s single-season passing record for a first-year player — it’s safe to say Luck exceeded just about all of them.

Luck threw for 205 yards Sunday, and his 7-yard touchdown pass to Reggie Wayne on third-and-goal late in the fourth quarter gave the Colts a 20-13 victory over the Kansas City Chiefs. That put them into the playoffs without worrying about anybody else.

“Would we have done it without him?” Colts interim coach Bruce Arians asked. “No.”

Luck broke Newton’s record of 4,051 yards passing in the second quarter. But it was extending his own rookie record for fourth-quarter comebacks to seven was more important.

The Chiefs had rallied behind Jamaal Charles’ 226 yards rushing to tie the game 13-13 heading into the fourth quarter. The Colts’ defense stuffed quarterback Brady Quinn on fourth-and-inches to give Luck a chance.

That’s all he needed.

After a miserable stretch in which he connected on 1 of 13 passes, the fabulous freshman calmly led Indianapolis (10-5) downfield. He completed a key pass to T.Y. Hilton on third down and made two nice throws to Wayne before hitting the veteran in the back of the end zone.

“We had so many opportunities all game, especially on third down, that we squandered,” Wayne said. “We wanted to get that done. That was the opportune time to do it.”

Darius Butler returned an interception 32 yards for the Colts’ other touchdown, helping them join the 2008 Miami Dolphins as the only teams to win at least 10 games after losing 14 or more the previous season.

Most of those wins have come under Arians, who has filled in admirably while Chuck Pagano underwent treatment for leukemia. Pagano is expected to rejoin the Colts this week.

“Mission accomplished. That’s all I can say,” Arians said. “Without getting emotional again, knowing that (Pagano) is going to be back Monday, the work week shouldn’t be as stressful.”

Charles’ big day included an 86-yard touchdown run on the first play of the second half. It was his second 200-yard game of the season, 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. His third career 200-yard game also set a franchise record, which he had shared with Larry Johnson.

Peyton Hillis added 101 yards on the ground for the Chiefs (2-13), who had 352 yards rushing in a losing effort — the first time that’s happened in NFL history.

A big reason why was Quinn, who was just 10 of 22 for 162 yards with two interceptions.

“This game was without a doubt, 100 percent on my shoulders,” he 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. Butler picked off the pass in stride, taking it untouched to the end zone for 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.