Josh Allen had four touchdowns as he completed 27 of his 36 passes for 320 yards, with the third-year quarterback again ably assisted by wide receiver Stefon Diggs, who had nine catches for 145 yards and three scores.
The game started quietly enough and the first quarter wrapped with the AFC East enemies tied at 3-3 before both sides scored early in the second to make it 10-9.
The Patriots were then kept scoreless as the visitors claimed four touchdowns and New England quarterback Cam Newton suffered the ignominy of being benched halfway through the third quarter.
The loss ensures the Patriots, who had already been ruled out of the post-season, will finish their campaign with a losing record for the first time since 1999, when Belichick joined forces with a rookie called Tom Brady.
That campaign more than 20 years ago was also the last time New England suffered a regular season sweep to the Bills, who can secure the No 2 seed in the AFC by winning in week 17 or if the Indianapolis Colts defeat the Pittsburgh Steelers.