Buffalo led 17-13 entering the fourth quarter, before New England scored 11 unanswered points down the stretch to secure the 24-17 win Saturday at Gillette Stadium in Foxborough, Mass.
The Patriots (12-3) have now won the AFC East for 11 consecutive seasons.
"It's a great reward, it's a great step for us and it's great to control the ability to do that, too," Brady told reporters. "Happy for us, our team, our coaches, our families and our fans, and hopefully we can build on it and go play great next week."
Brady completed 26 of 33 passes for 271 yards and one score in the win. Patriots running back Sony Michel had 101 total yards in the triumph.
Patriots running back Rex Burkhead fumbled on the game's opening drive, leading to a Bills field goal. The Patriots responded with an 11-play, 75-yard scoring drive. Brady threw an eight-yard touchdown pass to Matt LaCosse to cap off the drive, giving the Patriots a 7-3 advantage.
Folk gave the lead back to the Patriots with a 51-yard field goal in the third quarter. Allen hit John Brown with a 53-yard touchdown pass with 7:25 remaining in the third frame to give the Bills a four-point lead entering the final quarter.
Folk made a 20-yard kick at the start of the fourth quarter. Burkhead ended a seven-play, 59-yard drive with a one-yard scoring run to give the Patriots their final advantage with 5:06 remaining.
"That was a playoff game," Patriots cornerback Stefon Gilmore said. "We knew it was going to be tough. A lot of guys stepped up. It wasn't easy, but we stuck together and came out with a win."