The crowd were on the edge of their seats as Tucker unleashed the history-making kick, with the ball bouncing on the crossbar before eventually going over.
The previous record holder Matt Prater, who managed 64 yards in 2013, had earlier on Sunday attempted an 68-yard field goal in the Arizona Cardinals’ 31-19 win against the Jacksonville Jaguars, only for Jamal Agnew to collect the missed attempt and score a stunning 109-yard touchdown.
Chiefs head coach Andy Reid was taken to hospital after feeling ill following the game and was resting in a stable condition after evaluation by medical staff.
The New England Patriots were dealt an injury blow as running back James White came off with a hip problem in their 28-13 loss to the New Orleans Saints.
Younghoe Koo kicked the game-winning field goal at the death as the Atlanta Falcons beat the New York Giants 17-14.
Elsewhere, the Tennessee Titans won 25-16 against the Indianapolis Colts, the Cincinnati Bengals beat the Pittsburgh Steelers 24-10, the Cleveland Browns beat the Chicago Bears 26-6 and the Buffalo Bills beat the Washington Football Team 43-21.
Tom Brady was unable to power the Tampa Bay Buccaneers past the Los Angeles Rams, going down 34-24, while the Green Bay Packers scraped past the San Francisco 49ers by two points 30-28.
The Denver Broncos blanked the New York Jets 26-0 and the Las Vegas Raiders edged past the Miami Dolphins 31-28.