The Redskins (2-2) got all their points in the third quarter, erasing a 10-0 halftime deficit.
The Campbell-to-Moss play covered 59 yards. Washington also scored on a 17-yard pass from Campbell to Chris Cooley and a 42-yard field goal by Shaun Suisham
Campbell completed 12-of-22 passes for 170 yards.
Clinton Portis ran for 98 yards for the Redskins.
Josh Johnson tossed an 8-yard touchdown pass to Antonio Bryant and Nugent also kicked a 47-yard field goal for Tampa Bay (0-4).
Johnson was 13-of-22 for 106 yards, with one interception.