The Miami Dolphins produced a brilliant last-gasp touchdown to beat New England 34-33 and prevent the Patriots clinching a 10th successive AFC East title.
Miami, the last team to stop the Patriots winning the division, went 69 yards with the last action of the game for a touchdown that included two lateral passes.
Kenyan Drake was the last recipient and secured a dramatic victory that overshadowed Tom Brady’s latest record-breaking performance.
The Patriots quarterback had broken Peyton Manning’s record for the most touchdown throws in NFL history with his first of three scoring passes in the first half.
Brady found Julian Edelman in the first period to record his 580th touchdown throw and pass Manning’s score outright, before also connecting with Cordarrelle Patterson and Rob Gronkowski.
But former Patriot Brandon Bolden ran in two touchdowns and Brice Butler also reached the endzone before the Dolphins secured victory with Drake’s memorable moment.
The Kansas City Chiefs did manage to clinch a play-off place on Sunday as they produced some late drama of their own to earn a 27-24 overtime victory against the Baltimore Ravens.
The Chiefs were facing defeat with 89 seconds left as they trailed 24-17 and had a fourth and nine to convert, but quarterback Patrick Mahomes brilliantly connected with Tyreek Hill to extend the drive and it led to a Damien Williams touchdown.
But despite the Chiefs defence then forcing a turnover, Harrison Butker missed from 43 yards with a potential game-winning field goal.
Butker redeemed himself with a 35-yard field goal in overtime and the Chiefs defence kept Baltimore out to secure an 11th win of the season.
The New Orleans Saints clinched back-to-back NFC South titles and their place in the post season with a come-from-behind 28-14 victory against the Tampa Bay Buccaneers.
Tampa Bay led 14-3 at half-time but the Saints hit back as quarterback Drew Brees hit Zach Line from one touchdown before rushing for another, while Mark Ingram surged through for another score.
The Houston Texans saw their nine-match winning streak end at the hands of AFC South rivals the Indianapolis Colts.
Andrew Luck threw for two touchdowns as the Colts won 24-21 to move to within two games of their opponents in the battle for a play-off place.
The Green Bay Packers started life without Mike McCarthy with a 34-20 victory against the Atlanta Falcons, with Aaron Rodgers setting an NFL record for the most consecutive passes without an interception.
Rookie Saquon Barkley rushed for 170 yards and scored a 78-yard touchdown run as the New York Giants thrashed the Washington Redskins 40-16.
Third-choice Redskins quarterback Mark Sanchez completed just six passes for 38 yards and two interceptions before being replaced by Josh Johnson, threw for 195 yards and a touchdown and also ran for a touchdown.
Elsewhere, the Carolina Panthers suffered a fifth straight defeat as they lost 26-20 to the Cleveland Browns while the New York Jets beat the Buffalo Bills 27-23.
The Dallas Cowboys extended their lead at the top of the NFC East with an overtime win against division rivals the Philadelphia Eagles.
Amari Cooper scored his third touchdown of the game with just under two minutes left in the extra session to seal a 29-23 victory.
The Cowboys have now won five games in a row and have a two-game lead over the Eagles with three left to play.
The Chicago Bears surged ahead at the top of the NFC North as they stunned the Los Angeles Rams 15-6.
Chicago held NFL leading rusher Todd Gurley to a season-low 28 yards on 11 carries, while Rams quarterback Jared Goff posted a career-low 19.1 passer rating.
Meanwhile, quarterback Derek Carr completed his 16th career fourth-quarter comeback as the Oakland Raiders topped the Pittsburgh Steelers 24-21, throwing a six-yard touchdown pass to Derek Carrier with 21 seconds left.
George Kittle became the first tight end in 49ers history to reach 1,000 yards in the season as San Francisco overcame the Denver Broncos 20-14.
And Michael Badgley’s 59-yard field goal – the longest in franchise history – helped the Los Angeles Chargers beat the Cincinnati Bengals 26-21.
In the day’s other game, the Detroit Lions beat the Arizona Cardinals 17-3.