Stafford completed 25-of-42 attempts for 385 yards with an interception as the Lions took a victory in Washington for the first time in their 76-year history of road appearances there, going 0-22 during the span.
Joique Bell racked up 132 yards of total offense with a touchdown while subbing for the injured Reggie Bush as Detroit (2-1) rebounded from a loss last week at Arizona.
Calvin Johnson led the Lions' receiving corps, making seven grabs for 115 yards with a touchdown.
The Redskins (0-3), meanwhile, dropped a third straight to start the season for the first time since 2001.
Robert Griffin III picked up 326 aerial yards on 32-of-50 attempts but was intercepted and lost a fumble for Washington.