Tom Brady leads Patriots to third straight Super Bowl with 37-31 overtime win over Chiefs

The temperature dropped to 18 degrees with a wind-chill factor of 8 midway through the fourth quarter of Sunday night’s AFC championship game in Arrowhead Stadium, where a red-clad, goose-down, wool-cap-covered crowd of 77,034 was chilled to the bone.

The New England Patriots and Kansas City Chiefs were just getting warmed up.

A pair of high-powered offenses led by superstar quarterbacks at the opposite ends of their careers combined for 31 points and four lead changes in the final 7 minutes 45 seconds of regulation, sending a conference title game into overtime for the second time on this wildest of NFL Sundays.

From there, Tom Brady, the ageless wonder, the 41-year-old New England quarterback who has turned the last-minute, game-winning drive into an art form, took over.

The Patriots won the overtime coin toss and Brady marched them downfield, converting three huge third-and-10 plays on a 75-yard drive that ended with Rex Burkhead’s two-yard touchdown run and a 37-31 victory.

Brady’s heroics — he has engineered 43 game-winning drives in the fourth quarter or overtime in the regular season — sent New England to its third straight Super Bowl and an NFL-record 11th Super Bowl in franchise history. They will face the Rams in Atlanta on Feb. 3.

The Chiefs and 23-year-old gunslinger Patrick Mahomes, who was unable to get his hands on the ball in overtime after throwing for 295 yards and three touchdowns in regulation, were left out in the cold, their Super Bowl drought extending to a 50th season.

“You have to accept that this hurts,” said Mahomes, who threw for 5,097 yards and 50 touchdowns in his first season as a starter. “You put in work for this. You’re doing everything you can to get to the Super Bowl and win it.

“For this opportunity to fall short, it’s going to hurt.”

This is the ninth time in 19 years that Patriots coach Bill Belichick and Brady, who have won five titles together and are the winningest coach/quarterback tandem since 1970 with 207 regular-season victories, have gone to the Super Bowl.

Brady had his fingerprints all over this win, completing 30 of 46 passes for 348 yards and one touchdown and making several clutch throws in overtime.

“He was super cool,” Burkhead said of Brady’s demeanor on the final drive. “He’s been there so many times, it’s like second nature to him. He’s had the pressure, he’s been in those moments before, so all your trust and confidence is in him getting the job done, which he did.”

On a third-and-10 from his own 35-yard line in the extra period, Brady threw over the middle to sure-handed slot receiver Julian Edelman for 20 yards. On third and 10 from the Chiefs’ 45-yard line, Brady hit Edelman, who caught seven passes for 96 yards, with a 15-yard strike.

On third and 10 from the Kansas City 30, Brady hit tight end Rob Gronkowski, who caught six passes for 79 yards, on a quick slant for 15 yards. Though Sony Michel led New England rushers with 113 yards in 29 carries, it was Burkhead who covered the final 15 yards in three carries.

“Oh man, how many third-and-10s was that?” Patriots cornerback Jason McCourty said of the final drive. “As a defender, you’re just sitting there, and there’s no panic. I mean, no one was standing up. We’re all sitting on the heated benches — it was cold out — and you’re just watching it, almost in awe.”

New England dominated the first half, outgaining the Chiefs 245-32 in yards and 16-3 in first downs. They ran 42 plays compared to Kansas City’s 16 and held possession for 21:07 compared to 8:53 for the Chiefs.

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They led 14-0, they pressured Mahomes and contained explosive weapons, such as receiver Tyreek Hill, tight end Travis Kelce, and running back Damien Williams.

“They challenged us — they came up and played man [defense] — not a lot of teams have this year,” Mahomes said. “They put people in our face to see how we responded. The first half, we struggled. The second half, we found a way to win one-on-one matchups.”

Mahomes opened the third quarter with a 54-yard pass to Sammy Watkins and a 12-yard touchdown pass to Kelce that made the score 14-7. Stephen Gostkowski’s 47-yard field goal gave New England a 17-7 lead.

Mahomes capped a nine-play, 75-yard drive with a one-yard scoring strike to Williams to make the score 17-14 early in the fourth. Safety Daniel Sorenson’s interception of a tipped pass set up Mahomes’ 23-yard touchdown toss to Williams that gave the Chiefs their first lead, 21-17, with 7:45 left.

New England drove 75 yards in 10 plays, Michel bursting through a huge hole on a fourth-and-one from 10 yards out for a 24-21 lead, a touchdown that was set up by a spectacular, one-handed diving grab by Chris Hogan for an 11-yard gain on third and eight.

The Chiefs took advantage of a questionable pass-interference call on J.C. Jackson that gave them a first down on the Patriots’ 40. Mahomes hit Watkins on a wheel route for 38 yards, and Williams scored from two yards out for a 28-24 Kansas City lead with 2:03 left.

Mahomes then worked some last-second magic, completing a 21-yard pass to Spencer Ware and a 27-yard pass to Demarcus Robinson to set up Harrison Butker’s game-tying 39-yard field goal with 31 seconds left.

One coin flip, three clutch third-down Brady passes in overtime and one Burkhead touchdown run later, the Patriots, who were 3-5 on the road in the regular season, won in one of the league’s most hostile environments.

“That was a great way to end it,” Brady said. “I was probably as excited as I’ve been in a long time.”

Next stop: Super Bowl LIII.

mike.digiovanna@latimes.com

Follow Mike DiGiovanna on Twitter @MikeDiGiovanna