The score with 1:06 remaining in the third gave New England a one-touchdown lead and the Pats (8-5) held on to end a two-game slide.
New England has a one-game lead atop the AFC East, just ahead of Miami and the New York Jets, both 7-6 after winning their games. Miami downed Jacksonville 14-10 and the Jets defeated Tampa Bay 26-3.
Kevin Faulk ran 3 yards for a touchdown and Stephen Gostkowski kicked field goals of 48 and 47 yards for New England.
Brady, who has been bothered by injuries, completed 19-of-32 passes for 192 yards, with an interception, Laurence Maroney carried 22 times for 94 yards and Wes Welker had 10 receptions for 105 yards.
The Panthers (5-8) scored on a 41-yard pass from Matt Moore to Steve Smith and a 36-yard John Kasay field goal.
Moore was 15-of-30 passing for 197 yards and DeAngelo Williams ran for 82 yards on 13 carries for Carolina, which has lost three of its last four games.