The win was Detroit's first since December 2007.
Stafford and Bryant Johnson hooked up on a 21-yard touchdown pass that finished off a 99-yard drive in the first quarter.
Morris ran for a 2-yard score in the fourth quarter and Jason Hanson kicked field goals of 39 and 26 yards for the Lions (1-2) in the second.
Kevin Smith carried 16 times for 101 yards before leaving the game with an injury in the third quarter.
Jason Campbell was 27-of-41 for 341 yards, including scoring throws of 57 yards to Santana Moss and 4 yards to Rock Cartwright for the Redskins (1-2).