Griffin's only TD toss of the day came late in the third quarter and gave the Redskins a 17-14 lead after David Amerson had scored on a 45-yard interception return off Oakland's Matt Flynn before halftime.
Flynn's fumble in the fourth quarter led to another Washington score as Roy Helu, filling in for an injured Alfred Morris, secured the triumph with 14-yard TD run.
Griffin finished 18-of-31 passing for 227 yards as the Redskins (1-3) notched their first win of the season.
Flynn started for Terrelle Pryor, who sat out with concussion symptoms. He ended with 227 passing yards, including an 18-yard touchdown toss to Mychal Rivera for the Raiders (1-3).