Quarterback Josh Allen threw two touchdown passes to help the Bills move ahead of the Miami Dolphins.
Allen was 22 of 33 for 223 yards through the air as he became the first player in league history to record three seasons with 25 passing touchdowns and five rushing scores.
"I thought we played really well tonight," Allen told NFL.com. "Honestly, it's only 24 points, but our defense played fantastic ball.
"We didn't feel like we had to press and make any mistakes. There are a few plays we would like to have back, but again these are good wins in the division, away, it's hard to win in this league. We'll learn from this one and move on."
This was the third-straight win for the Bills who now set their sights on divisional rivals the New York Jets on December 11.
"We know these games that are coming up, they matter," Allen told ESPN.
"The ones in December and January, they matter. We've got to find ways to go win some football games."
The highlight for the Patriots came on their opening drive when cornerback Marcus Jones took his first offensive snap of the season, catching a pass from quarterback Mac Jones before finding a gap to race away for a 48-yard touchdown.
New England will be looking to return to winning ways when they face a struggling Arizona Cardinals side on December 12.