Westbrook scored with 3:16 remaining in regulation, and then scored again with just 2:18 left, while Donovan McNabb completed 20-of-28 passes for 251 yards and four touchdowns for the Eagles.
Westbrook finished with 100 yards and three touchdowns on 20 carries.
Jason Campbell threw a career-high three touchdown passes on 23-of-34 passing for Washington.
Former Eagles receiver James Thrash caught two touchdown passes and picked up 85 yards, playing in place of injured Redskins' receiver Santana Moss.
Celebrity Families of 2014 [PHOTOS]