The Redskins let a 17-0 lead slip away and the Bucs took the lead with 2:07 left on a 20-yard pass from Jonathan Crompton to Armando Allen. Clemens then drove the Redskins 74 yards in five plays to the winning score.
Backup Tampa Bay quarterback Rudy Carpenter was 9-of-18 for 211 yards and a touchdown -- a 96-yard scoring throw to rookie Ed Gant.
Washington built its early lead thanks in part to a 95-yard punt return by Brandon Banks.
The Redskins went 3-1 during the exhibition season and Tampa Bay was 2-2.
Washington starts the regular campaign at home against the New York Giants. The Bucs will host Detroit.