Brandon Meriweather put the Patriots ahead after just two minutes, running home a great interception, and his side added to the lead with touchdowns from Wes Welker and Sam Aiken, who snapped up Brady's 53-yard pass.
The Buccs — technically the home side — scored when Antonio Bryant caught Josh Johnson's 33-yard pass just before half time.
But the Patriots hammered home their advantage with further touchdowns from Benjamin Watson and Laurence Maroney.