Cundiff's clutch field goal came with 3 seconds remaining in the fourth quarter and made up for earlier missed tries of 41, 57 and 31 yards.
Robert Griffin III connected on 26-of-35 passes for 323 yards and also scored a rushing TD for the Redskins (2-2), who broke a two-game losing skid.
Alfred Morris led the Washington ground game with 113 yards and a score on 21 carries.
The Buccaneers (1-3), meanwhile, dropped their third straight despite a good game from Josh Freeman (24-of-39 passing, 299 yards, touchdown, interception).
Notable deaths of 2014 [PHOTOS]