KANSAS CITY, Mo. — Over the last three decades or so, the Cincinnati Bengals have dabbled in wretched football and entertaining football, tedious football and effective football, but not until this postseason had they managed to play the brand of football they desired most.

After going 31 years between playoff victories, a stretch of futility unmatched in major professional sports, the Bengals have now triumphed three times in two weeks. Their latest, craziest conquest vanquished the reigning A.F.C. champion Kansas City in a second-half comeback that the good folks of southwestern Ohio and neighboring areas will hail for years.

And the final score — 27-24, in overtime, secured on Evan McPherson’s 31-yard field goal — will linger, too, on their tongues, numerical confirmation that the Bengals have played, yes, winning football. They tamed the cauldron of cacophony in Arrowhead Stadium to advance to the Super Bowl. Not since Ickey Woods shuffled and Boomer Esiason flung lefty passes and David Fulcher prowled the secondary, in the 1988 season, had Cincinnati reached the final game of the season.

“This is a special team that’s capable of doing special things,” Coach Zac Taylor said, “and we believed from the get-go whether people believed in us or not.”

The group that returned the Bengals to that euphoric state is led by a cigar-smoking, Cartier-sunglasses-wearing quarterback who feels neither pressure nor pain. Joe Burrow led Cincinnati to 21 consecutive points, erasing a 21-3 deficit. Then he calmly took the Bengals downfield in overtime following Patrick Mahomes’s interception on the opening possession, after Kansas City had evened the score at 24-24 with a field goal as regulation expired.

“If you want to do the things that we want to do,” Burrow, who finished 23 of 38 for 250 yards, two touchdown passes and an interception, said last week of Kansas City, “that’s the team you’re going to have to beat every single year.”

Kansas City had dropped only one game since Halloween — a 34-31 defeat to the Bengals in Cincinnati on Jan. 2 — and precedent suggested that Sunday would proffer the opposite result. Over the last three years, it had won all five rematches against teams it lost to earlier in the season while scoring more than 39 points per game.

The most recent payback occurred at this same venue last week, when Kansas City kindled an absurd comeback — a three-play, 44-yard, 13-second field goal drive — to tie Buffalo at the end of regulation before winning the divisional round game in overtime.

As then, Kansas City won the overtime coin toss. But instead of driving for the clinching touchdown on Sunday, Mahomes, looking downfield for Tyreek Hill, threw an interception — his second of the game — that bounced off the hands of Hill and Cincinnati’s Jessie Bates III and into those of Bengals defensive back Vonn Bell.

Taking over at the Bengals’ 45-yard line, Burrow drove the Bengals deep into Kansas City territory, with McPherson — who made all four of his field goal attempts against both Las Vegas and Tennessee in the previous rounds — drilling his fourth long and true, sending his teammates spilling onto the field.

Sunday’s game unfolded as if adhering to the basic template from the teams’ Week 17 meeting, with Mahomes flaunting his magnificent, improvisational and unstoppable version of football in the first half before the Bengals rediscovered their compass.

And just as in that earlier game, Kansas City amassed a first-half lead that it eventually ceded. In the early-January meeting, Kansas City led by 14 points before succumbing, 34-31. On Sunday, Kansas City headed into halftime leading, 21-10, on three Mahomes touchdown passes. The margin could have been — should have been? — wider if not for both a curious play call and excellent tackling by Bengals cornerback Eli Apple.

With five seconds left in the first half, no time outs and the ball at the Cincinnati 1-yard line, Coach Andy Reid, eschewing the close field-goal attempt, tried to blowtorch the Bengals out of commission. Mahomes flipped a pass to Tyreek Hill at the 5-yard line, and Apple — after committing the pass-interference penalty that gave Kansas City the ball by the goal line — preserved the 11-point deficit by standing him up.

It was the first of six consecutive defensive stops by the Bengals, who converted the third into McPherson’s second field goal, and the fourth into the touchdown that evened the score at 21-21.

In desperate times, Burrow knows he can turn to the Bengals’ best receiver — his old pal from Louisiana State — and with 14 seconds left in the third quarter he zipped a nifty back-shoulder toss to Ja’Marr Chase. Trent Taylor wiggled free off the line to catch the 2-point conversion.

Last week, Burrow proclaimed his disgust with what he called the “underdog narrative” surrounding the Bengals, demanding the team be taken seriously. Already he had changed the team’s slogan, to “It Is Us” from “Why Not Us?”, and his teammates agreed.

“That’s not really the idea you want in your head when you step in the ring,” left tackle Jonah Williams said last week. “It’s not, ‘Why can’t I knock this guy out?’ It’s, ‘I’m going to knock this guy out.’ It’s a much more powerful attitude to have.”

The most unassailable truth in the N.F.L. these last three seasons had tended to manifest itself right around this time of year: No matter how Kansas City plays early in the season, and no matter how Kansas City plays in the middle of the season, and no matter how Kansas City plays late in the season, it ends the A.F.C. championship game at home, in rapture.

It happened two years ago, and it happened last year, but not this year — not on Sunday. The Bengals — the Cincinnati Bengals — knocked out mighty Kansas City and will play in the Super Bowl.