The defensive end out of California set a franchise record with 4 1/2 sacks in the game, surpassing the previous three-way tie between Julius Adams, Tony McGee and Mike Hawkins, who each had four sacks in a single game.
Sunday's game marked the third time this season Carter has posted two or more sacks. He leads the Patriots with nine sacks this season.
Carter's previous career-high sack total was 2 1/2 in a game against the Panthers on Oct. 11, 2009, when Carter was a member of the Redskins.
Carter last won the player of the week award as a rookie with the 49ers. He had six tackles and two sacks against the Saints on Jan. 1, 2002 to claim the award for the first time.