The pass that turned out to be the game-winner came with 3:29 to play, completing a comeback for the Redskins, who trailed 24-15 after three quarters.
Clinton Portis scored two rushing touchdowns, and Chris Horton intercepted two passes and recovered a fumble for Washington (1-1).
Campbell finished with 24 completions for 321 yards.
Moss had seven catches for 164 yards and Portis ran for 96 yards, including his two touchdowns, on 21 carries.
Drew Brees passed for 216 yards and a touchdown and Reggie Bush had a 55-yard punt return for a touchdown for the Saints (1-1).