Tom Brady added another chapter to his Hall of Fame legacy Sunday night, leading the New England Patriots to a dramatic 37-31 overtime victory over the Kansas City Chiefs in the AFC Championship game.

Rex Burkhead's two-yard touchdown run on the first possession of the extra period set up a matchup between the Patriots and the Los Angeles Rams in Super Bowl 53 in Atlanta Feb. 3. The Patriots advanced to their ninth Super Bowl with Brady at quarterback and Bill Belichick as the coach and their 11th in franchise history, extending their NFL-record mark. Brady, 41, will also break his own record as the oldest quarterback to start a Super Bowl.

New England also became just the third team to reach at least three consecutive Super Bowls, joining the Miami Dolphins (1971-1973) and Buffalo Bills (1990-1993).

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"Overtime, on the road against a great team," Brady said. "[The Chiefs] had no quit. Neither did we. We played our best football at the end. I don't know, man, I'm tired. That was a hell of a game."

Sunday night was not Brady's finest statistical performance. He threw two interceptions, the first of which came with New England a yard away from a second-quarter touchdown that would have put them up 14-0 early. The second, midway through the fourth quarter, helped set up Patrick Mahomes' 23-yard touchdown pass to Damien Williams, which gave Kansas City their first lead of the evening at 21-17.

But when time was winding down, when the money was on the table and big throws needed to be made, Brady was as unflappable as ever. First, he led a 10-play, 75-yard touchdown drive that ended with a 10-yard touchdown run by Sony Michel to put New England back on top, 24-21. Then, after the Chiefs took a 28-24 lead on a two-yard run by Williams with 2:04 to go, Brady took the Patriots 65 yards in six plays, a march that ended with Burkhead crashing over from four yards out to make the score 31-28, Patriots with just 39 seconds left.

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Finally, after the Chiefs forced overtime with a 39-yard Harrison Butker field goal, the Patriots won the coin toss and Brady and co. made sure that Mahomes would not see it again. Facing third-and-10 on three separate occasions, Brady completed a 20-yard pass to Julian Edelman, a 15-yard pass to Edelman and a 15-yard pass to Rob Gronkowski. The third big conversion put the ball at the Kansas City 15-yard line and two plays later, Burkhead was in the end zone for the winning score.

Brady finished the day completing 30 of his 46 passes for 348 yards and a touchdown in addition to the two interceptions. Mahomes, who came so close to ending Kansas City's 49-year wait for a Super Bowl appearance, completed 16 of his 31 passes for 295 yards and three touchdowns. The bulk of the completions and yardage came in a sparkling second half for the Chiefs offense, which scored 31 points after being held to 32 total yards in the first half, after which they were lucky to only be down 14-0. It was the first time Kansas City had been shut out in any half this season.

Just as they did last week in manhandling the Chargers early and cruising, the Patriots delivered a message -- and a touchdown -- on their first series. It was a classic, covering 80 yards in 15 plays and using up more than eight minutes. Michel rushed for 32 yards and scored from the 1.

A familiar look continued on the next drive. Oh, it was shorter in length and distance, but took up the rest of the opening quarter, in which New England had the ball for 12:35. This 56-yard march as Mahomes watched helplessly from the sideline didn't culminate in the expected, though. Brady's third-down pass from the 1 for Gronkowski was short and Reggie Ragland picked it off.

Brady had never thrown an interception from the 1.

When the Chiefs finally got a trademark big play on Mahomes' 42-yard completion to Hill, it went for naught. Mahomes overthrew a wide-open Williams near the end zone, then took a 14-yard sack to send KC out of field goal range.

Big mistake.

The Patriots kept dominating the line of scrimmage, Brady took them 90 yards and connected with Phillip Dorsett over sloppy coverage by Steven Nelson to make it 14-0 with 27 seconds left in the half.

But Kansas City's zero disappeared quickly in the third quarter. Finally given solid protection, Mahomes unleashed a 54-yard completion to Sammy Watkins over All-Pro cornerback Stephon Gilmore. He then hit another All-Pro, tight end Travis Kelce, on a slant to make it 14-7 -- and awaken the slumbering crowd.

But one of several bad decisions further damaged Kansas City when Tyreek Hill, the All-Pro flex player, retreated deep in Chiefs territory returning a punt. Eventually, KC had to punt and the Patriots had excellent field position, setting up a 47-yard field goal by Stephen Gostkowski.

Not one to be shy about innovation, Mahomes sidearmed a throw to Watkins for 10 yards on a third down, then a dump-off to Williams covered 33. Kelce drew a pass interference call on J.C. Jackson in the end zone, and Mahomes threw a strike to Williams for the score.

Although the Chiefs were on their heels much of the night, they were down only 17-14.

As in the NFC title game, some scrutiny will fall on the officiating. The Patriots received the benefit of the doubt on two replay reviews, one of which kept alive the late drive that ended in Michel's touchdown run. There may also be a move to tweak the overtime rules to give both teams a possession even if a team scores a touchdown on the first drive.

With New England clinging to their three-point fourth-quarter lead, an apparent muff by the usually reliable Edelman was overturned, prompting raucous booing and some demonstrative arguing from the usually laid-back Andy Reid. Two plays later, Edelman deflected a Brady pass into the arms of safety Daniel Sorensen. His 22-yard return set up Kansas City at the Patriots 23, and Williams scored the second of his three touchdowns to put the Chiefs on top.

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On the ensuing drive, Chris Hogan's diving one-handed catch on a third-and-eight throw from Brady was upheld on review despite it appearing to touch the ground. Michel scampered into the end zone six players later on fourth and one.

Sunday's dramatics marked the first time that both conference championship games went to overtime and the first time that both visiting teams had advanced to the Super Bowl since the Baltimore Ravens and San Francisco 49ers did so after the 2012 season.

The Associated Press contributed to this report.