Kansas City wins in overtime with a Kelce touchdown catch.

“That’s the type of level that we want to be; in order to be the best, you go to beat the best,” Allen said. “And they’ve really been one of the, if not the best team in the last four years.”

Allen played well Sunday, throwing for 329 yards and four touchdowns, all of them to Davis, two of them in the fourth quarter. He also rushed for a team-high 68 yards. His only downfall was that he did not have the ball last. He could only watch from the sideline as Kansas City won the coin toss before overtime, leaving him unable to respond to Kelce’s game-winning touchdown. It was a disappointing end to a successful season in which the Bills won the A.F.C. East for the second straight year and finished with the N.F.L.’s top-ranked defense.

“I know the fans are disappointed, and I wish I could take it off of them,” Bills Coach Sean McDermott said. “I wish I could take it off the team, but we can’t. What doesn’t kill you should only make you stronger. It’s going to take some time, but it will make us stronger.”

Sunday night’s game mimicked the 2018 season’s A.F.C. championship game, when Mahomes saw Tom Brady and the Patriots march down the field and win in overtime. Mahomes joked that he would “take the win,” but that he would have loved to have seen Allen on another possession.

“Whenever you have two teams going back and forth the way that we were going, it kind of stings that you can’t see the other guy go,” Mahomes said.

Kansas City, too, experienced a pendulum of emotions as the game concluded. Reid and the players credited Mahomes’s resolve and the team’s preparation. In his postgame news conference, Hill said the team practices late-game situations on Fridays, and that resolve showed on Sunday. Mahomes demonstrated his greatness, Hill said, by driving Kansas City 44 yards in three plays with 13 seconds left to set up Butker’s game-tying kick. On the sideline before that sequence, Reid told Mahomes: “When it’s grim, go be the grim reaper.”

“This is just another step to get him into the Hall of Fame,” Hill said.

The game in some ways resembled Kansas City’s season. The team started 3-4 and looked vulnerable, as defenses found ways to contain its downfield strikes with zone coverage. But it rebounded, losing only one game since November and earning the No. 2 seed in the conference. Buffalo used some of those defensive strategies, but Mahomes was patient, relying on shorter throws and scrambling through open holes. In the rushing attack, Clyde Edwards-Helaire, Jerick McKinnon and Mecole Hardman combined for 115 yards. It was a complete performance, Mahomes said, that he will not forget.

“I’ll remember it forever,” he said.