The Buccaneers built a 23-7 lead early in the second half and fought off a Patriots' comeback bid while improving to 2-1 in the exhibition campaign.
Josh Freeman threw for 102 yards and Tampa Bay rookie running back Doug Martin ran for a score. Both Martin and Barron were taken in the first round by the Buccaneers.
Freeman completed 10-of-19 passes and Martin picked up 53 yards on 13 carries. Backup quarterback Dan Orlovsky threw an 8-yard touchdown pass in the fourth period.
Brady played into the third quarter, during which he drove New England 84 yards in eight plays and hit Rob Gronkowski with a 16-yard scoring pass.
The New England quarterback finished 13-of-20 for 127 yards. Backup Ryan Mallett threw for two touchdowns in the fourth period.
The Patriots are 1-2 in the pre-season.
Notable deaths of 2014 [PHOTOS]