Chiefs tight end Travis Kelce celebrates with teammates after catching an 8-yard touchdown pass in overtime to give Kansas City a 42-36 win over the Buffalo Bills in an AFC divisional playoff game Sunday night. Charlie Riedel/Associated Press

KANSAS CITY, Mo. — In a never-say-die showdown between two of the NFL’s top teams and two of its bright young quarterbacks, the Bills and Chiefs played a classic Sunday night decided by one them calling tails and the other making him pay for it.

Josh Allen’s decision on the overtime coin toss was his only mistake for Buffalo all night.

Patrick Mahomes promptly marched Kansas City downfield against the NFL’s top-ranked but exhausted defense and found Travis Kelce in the corner of the end zone from 8 yards, giving the Chiefs a memorable 42-36 victory.

Kansas City earned a spot in its fourth consecutive AFC championship game.

“The guys didn’t flinch,” Chiefs Coach Andy Reid said. “You talk about an epic game, well, that’s the way the players took it. They had tremendous respect for Buffalo and they knew it was going to be a battle and they kept going.”

What was Reid’s advice for Mahomes when the Chiefs were up against it?

“When it’s grim, be the grim reaper, and go get it,” Reid said. “He made everyone around him better.”

Indeed, the lead changed hands three times in the final two minutes of regulation before Harrison Butker, who earlier had missed a field goal and extra point, drilled a 49-yarder for Kansas City as time expired to force overtime.

The Chiefs won the coin toss and Mahomes took care of the rest.

“I’ll remember this for the rest of my life,” Mahomes said.

He finished with 378 yards passing and three touchdowns, including a 64-yarder to Tyreek Hill during the thrilling final minutes of regulation and the clutch throw to Kelce that sent players streaming off the bench.

“We got tremendous leaders on both sides of the ball, whether it’s offense, defense or special teams,” Hill said. “Nobody panicked. Nobody was like, ‘Oh, the game is over, there’s 13 seconds left.’ We just made plays.”

Allen did everything he could to prevent another season-ending loss in Arrowhead Stadium. He threw a go-ahead touchdown pass to Gabriel Davis with 1:54 left in the regulation, then another to Davis – his playoff-record fourth TD catch of the game – with 13 seconds remaining.

He finished with 329 yards passing, and Davis with eight catches for 201 yards, but the Bills – who had beaten the Chiefs in October – lost their ninth straight road playoff game since their last victory in the 1992 season’s AFC championship game.

“They made a couple more plays than we did obviously down the stretch,” Bills Coach Sean McDermott said. “The guys played their guts out, and you got to do a little better on the last couple of plays there.”

In a playoff game for the history books, the Bills and Chiefs played 58 minutes that few will remember, and about two minutes and an overtime that few will forget.

The Chiefs were leading 26-21 when Allen, who had been nearly perfect all night, connected with Davis for the third time in the game – a fourth-and-13 dart that gave the Bills the lead.

Not to be outdone, the Chiefs answered when Mahomes found Hill over the middle. The fleet-footed wide receiver ran away from cornerback Levi Wallace for a 64-yard touchdown that gave Kansas City the lead back.

Then it was the Bills’ turn. Allen threw a 28-yard pass to Davis, hit him again for 12 yards, then found Emmanuel Sanders to give Coach Sean McDermott’s team a chance with 17 seconds on the clock.

Allen hit Davis right between the numbers, their 19-yard strike giving him the postseason-record, but not the victory.

Mahomes wasn’t done conjuring up playoff magic. He found Hill for 19 yards, then hit Kelce for 25. That gave Butker a chance to try a 49-yarder into a slight, chilly breeze as time expired.

Naturally, it split the uprights to send the game to overtime – a fitting way to end a divisional-round weekend filled with last-second heroics.

INJURIES

Bills: Cornerback Micah Hyde left because of an undisclosed injury he sustained on the final play of regulation.

Chiefs: Tyrann Mathieu left on the opening drive because of a concussion after the Pro Bowl safety was hit by teammate Jarran Reed’s knee. … Cornerback Charvarius Ward was hurt trying to tackle Allen with 5 1/2 minutes left in regulation.


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