Two of the scoring passes fired by Brady (21-of-35, 296 yards) went to Aaron Hernandez, who finished with eight catches for 58 yards, while Brandon Lloyd also caught a TD pass and recovered a fumble in the end zone for the victors.
Stevan Ridley contributed 72 rushing yards with a score as New England (10-3) pulled to within one game of Houston (11-2) for the best record in the AFC.
Matt Schaub was limited to 19-for-32 efficiency with 232 yards and an interception for the Texans, who saw their six-game winning streak snapped.
Arian Foster managed just 46 yards with a touchdown on 15 carries in the loss.
Swim Week Miami Beach 2014 [PHOTOS]