New England Patriots quarterback Tom Brady (12) celebrates after defeating the Kansas City Chiefs in the AFC Championship NFL football game Sunday in Kansas City, Missouri. Credit: Charlie Neibergall | AP

KANSAS CITY, Missouri — The fervor of the hometown fans painted this frozen brown tundra red — and not just any red, either, but a bold primary color, the most vivid red imaginable, the kind of red that came from a heart artery. Even the opera house and the statues in the plazas wore Kansas City Chiefs red, and as far as the eye could see outside Arrowhead Stadium, the tailgaters huddled over their burning red coals while a frigid plains wind blew the barbecue smoke sideways.

But all that red became the color of heartbreak, because this AFC championship game turned on a coin flip in overtime that put the ball in the hands of Tom Brady and the drably immortal New England Patriots.

That’s what it came down to after all the things overturned and squandered, the weird switchbacks in momentum and penalty-aided drives, the spectacular snaring catches and tipped-ball interceptions, and above all the sorcery of that man in red, Patrick Mahomes, who spun things out of nothing to rally his Chiefs from a 10-point deficit in the fourth quarter. That quarter rendered all that came before it so irrelevant and included four lead changes before that classic, inexorable, 75-yard drive by Brady and the Patriots settled it, 37-31, in overtime. “It took everything,” Brady said.

They were a defiant and uncannily tough outfit, an organization that managed to feel like “the odds were stacked against us,” as Brady said, even though they will be going to their ninth Super Bowl since he was drafted in 2000 and have been playing for championships for “my entire life pretty much,” the 23-year-old Mahomes said. They battled the cold, and all that howling red, and a large measure of doubt: For all their success, they hadn’t won a road playoff game since 2007, and plenty of people said their day was done. But “give us a ball and a field, and we’ll be there,” linebacker Dont’a Hightower had said.

[Patriots nip Chiefs in overtime, advance to third straight Super Bowl]

It wasn’t a great game; it was a strange game, made stranger by some incoherent officiating and untimely yellow flags, which included a phantom roughing-the-passer call when the Chiefs apparently mussed Brady’s ascot. But it was a great dynamic, a classic on-field narrative between bold youth and aged maturity. It matched an electric shock of a young man in Mahomes, who was playing in just his 19th NFL game, and the 41-year-old Brady, who is going for his sixth Super Bowl title and who looked so timelessly statuesque on that final drive that he should have been wearing a tuxedo.

They went at two different paces, in two different styles. Mahomes was quicker, more improvisational, jazz. With that upturned pixie smile and sprig of hair and crazy loose power line of an arm and indefatigable confidence, he was the most alive player on the field. He brought the Chiefs so tantalizingly close that it left them with “an ache,” coach Andy Reid said.

Brady, by contrast, was sedate, unhurried and unhassled, even as he weathered two interceptions and the game’s major reversals, and the Chiefs’ comebacks time and again. The Patriots had a magnificent first quarter in which they held Mahomes and the Chiefs to just 32 yards. Their best defense was their offense, which kept the kid off the field as the Patriots dominated the ball for more than 21 minutes of the first half to lead 14-0.

But in the second half, Mahomes performed like the genius kid who cribs for the test and gets an A. The Chiefs came out of the tunnel to score so quickly that it snatched the breath out of your throat, Mahomes covering the final 66 yards in just two plays through the air. The kid was a show within the show, wriggling out of the clutches of the Patriots time and again, jerking a shoe or a shoulder away from a defender to launch big parabolas downfield or make a throw from his belt.

After so many debatable plays and arguable events, it came down to that coin toss. As soon as it came up heads to give Brady and the Patriots the first possession in overtime, safety Devin McCourty believed they had it won. “I saw this before,” he thought. “I know what happens at the end of this one.”

That unhurried rhythm of Brady’s took over again. “You got any touchdown plays left on that call sheet?” Brady asked offensive coordinator Josh McDaniels lightly, before he jogged back on the field.

“I do,” McDaniels answered.

[Tom Brady seems to think that ‘everyone thinks we suck’]

But it was Brady who made the calls work, who stood there so composedly three times on third and 10, only to unfurl those languid-seeming throws, two to Julian Edelman and one to Rob Gronkowski, before Rex Burkhead finally finished the thing off with his 2-yard punch into the end zone.

“It’s in his DNA,” Edelman said. “If there is a clutch gene, he’s got it.”

What Mahomes and Brady had in common from their opposite ends of the age spectrum was their wholeheartedness, their heedless exhaustion of themselves. That was worth closely attending to, amid all the frantic action around them — the size of their wagers upon themselves, their lack of hesitancy on that frozen gaming table. Underneath their performances was the willingness to court pain and inner mortification. “It hurts,” Mahomes said simply afterward. Which is of course the price that lies at the end of any heartfelt undertaking.