After a quiet start to the game, Patriots kicker Stephen Gostkowski had a chance to give the visiting team the lead, but he missed for the first time this season to leave the scores level.
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Orton quickly put the error behind him though, tossing the ball down the middle for Robert Woods to score his first touchdown of the season.
Gostkowski added a couple of field goals to put the Patriots back in front before half time before Brian Tyms added a score early in the third quarter.
The Bills kept the scores close heading into the fourth quarter as Fred Jackson added his first rushing touchdown of the season.
Orton found Chris Hogan to cut the lead again with just over five minutes to play, but Brady connected with LaFell again late on to end any hopes of a Buffalo comeback.
The result means that the Patriots leapfrog the Bills to top the division with a 4-2 record so far this season.