Sunday night's contest copied the NFC Championship game, as both conference title matchups went to overtime for the first time in a single postseason. Earlier in the day, the Los Angeles Rams defeated the New Orleans Saints 26-23 in OT to advance to Super Bowl LIII.
"Overtime, on the road against a great team, they had no quit but neither did we," Brady said after the game. "We played our best football at the end. I don't know, man. I'm tired. That was a hell of a game."
The Patriots (13-5) raced out to a 14-0 lead in the first half after a 1-yard touchdown run by rookie tailback Sony Michel and a 29-yard scoring pass from Brady to receiver Phillip Dorsett.
Kansas City's (13-5) first drive of the second half ended with quarterback Patrick Mahomes connecting with tight end Travis Kelce for a 12-yard touchdown. Patriots kicker Stephen Gostkowski booted a 47-yard field goal to give New England a 17-7 lead late in the third quarter.
Chiefs running back Damien Williams, who filled in for the released Kareem Hunt, scored the first of his three fourth-quarter touchdowns on the first play of the final frame. Mahomes found Williams for a 1-yard score to cut the Chiefs' deficit to 17-14.
Williams added a 23-yard receiving touchdown that gave Kansas City its first lead of the game with 7:45 left in the fourth. Michel responded with his second touchdown, a 10-yard run, to give the Patriots a 24-21 advantage.
Williams ran in from two yards out to retake the lead, but Burkhead's 4-yard touchdown run with 39 seconds left put the Patriots ahead 31-28.
Mahomes directed a drive to force overtime, ending with kicker Harrison Butker's 39-yard field goal with eight seconds remaining.
The Patriots won the overtime coin toss and used Burkhead's 2-yard plunge to reach another Super Bowl.
Brady threw for 348 yards on 30-for-46 passing with one touchdown and two interceptions. Michel ran 29 times for 113 yards and two scores. Burkhead added 12 rushes for 41 yards and two additional touchdowns.
Mahomes was 16-for-31 passing for 295 yards, three touchdowns and no picks. Williams had 10 carries for 30 yards and a rushing touchdown. He added five catches for 66 yards and two receiving scores.
The Patriots head to Atlanta to face off against the Rams (15-3) in Super Bowl LIII on Feb. 3 at Mercedes-Benz Stadium.