KANSAS CITY, Mo. — Every sport needs a marquee rivalry.

Boxing had Muhammad Ali and Joe Frazier. The N.B.A. had Michael Jordan and the Chicago Bulls countering Isiah Thomas and the Detroit Pistons. Tennis has Novak Djokovic, Rafael Nadal and Roger Federer.

In this age of the N.F.L., fans are witnessing the flourishing of Patrick Mahomes and Josh Allen.

The two young quarterbacks for Kansas City and the Buffalo Bills engaged in a thrilling battle on Sunday night as they went throw for throw in the A.F.C.’s divisional round, exchanging leads and accumulating yards as if it were an elementary schoolyard game at recess. The game was so exciting that it needed more time, the referee saying “great job so far” with a hint of sarcasm in his voice.

Harrison Butker kicked a 49-yard field goal to send the game to overtime after both teams exchanged the lead three times in just under two minutes. The contest finally concluded when Mahomes connected with Travis Kelce near the sideline for an 8-yard touchdown, leaving Kansas City with a 42-36 win at Arrowhead Stadium. Mahomes took off his helmet and ran into the end zone to meet Kelce as the wackiness of this game ended and officials confirmed the catch by replay.

“We were all just part of one of the better games in the National Football League,” Kansas City Coach Andy Reid said in his postgame news conference. The Chiefs will now play the Cincinnati Bengals for the A.F.C. championship next week, becoming the first team in league history to host four consecutive conference championship games.

The Bills and Kansas City rattled off highlight-reel plays as if they were ordinary. With 13 seconds remaining, Allen found Gabriel Davis uncovered in the end zone, completing a 19-yard touchdown pitch-and-catch. With 62 seconds remaining, Mahomes found the speedy Tyreek Hill open in space on an in-breaking route. He caught the ball and sprinted untouched for a 64-yard touchdown. In total, 25 points were scored in just under two minutes.

“If you’re not going to go down fighting, then you don’t deserve to be here,” Mahomes said in his postgame news conference.

The two quarterbacks have now dueled three times in the last calendar year. Mahomes bested Allen in last season’s A.F.C. championship game, 38-24, and after throwing for 325 yards and three touchdowns, hoisted the conference trophy at Arrowhead for the second consecutive season. As Kansas City celebrated, Bills receiver Stefon Diggs watched alone on the sideline while red, yellow and white confetti fell.

Buffalo got revenge this season in Week 5, when the Bills won, 38-20, giving Sunday night’s meeting the added drama of a tiebreaker. Both Allen, 25, and Mahomes praised each other in the past week, but Allen acknowledged that he was under more pressure to win, as Mahomes, 26, had already played in three A.F.C. championship games and won a Super Bowl.

“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.