Bradford finished with 196 aerial yards -- his favorite target was Lance Kendricks, who hauled down four passes for 119 yards, including an 80-yard touchdown grab.
Steven Jackson picked up 81 rushing yards with a score on 19 carries as the Rams (7-7-1) rebounded from a 36-22 loss to Minnesota last week and recorded their fourth win in five contests.
The Buccaneers (6-9), meanwhile, dropped their fifth straight despite 372 aerial yards from Josh Freeman, who completed 30-of-54 passes.
The Tampa Bay quarterback, however, was intercepted four times.
Mike Williams led the Bucs' receivers with seven catches for 132 yards and a touchdown.