Rookie De’Von Achane ran for 203 yards, two touchdowns and collected a touchdown pass from Tua Tagovailoa – who completed his first 17 passes – while fellow running back Raheen Mostert ran for three touchdowns and caught another.
Coach Mike McDaniel opted against a last-ditch field-goal attempt which would have broken the record of 72 points set by Washington against the Giants 57 years ago.
Josh Allen threw for one touchdown and ran for another as the Bills defence sacked home quarterback Sam Howell nine times.
Howell threw four interceptions, once of which was returned for a touchdown by AJ Epenesa – as the Commanders went scoreless until a field goal with 46 seconds left on the clock.
Swift cheered on from a suite at the invitation of Chiefs tight end Travis Kelce, with whom she has been romantically linked and who also grabbed a touchdown pass from Mahomes.
The Raiders, who trailed 23-7 going into the final quarter, cut the deficit to eight points but opted to take a field goal on fourth and four in the closing moments.
Dallas Cowboys’ impressive start to the season hit came to an abrupt end as they lost 28-16 at Arizona Cardinals, Joshua Dobbs throwing for a touchdown and 189 yards to secure his first win as a starting quarterback in his seventh NFL season.
Quarterback Derek Carr was forced off with a shoulder injury as the New Orleans Saints coughed up a 17-0 lead to lose 18-7 to the Green Bay Packers while Kenneth Walker II rushed for a pair of touchdowns as the Seattle Seahawks won 37-27 over the winless Carolina Panthers.
The Minnesota Vikings are also 0-3 after they went down 28-24 to the Los Angeles Chargers, Justin Herbert completing 40 of 47 passes – a franchise record 18 of them to Keenan Allen – for 405 yards and three touchdowns.
Matt Gay kicked four field goals from more than 50 yards, including the game winner in overtime from 53 yards, as the Indianapolis Colts won 22-19 to inflict a first defeat of the season on the Baltimore Ravens.