Jay Cutler led the Bears with 122 yards on 7-of-13 passing.
Backup quarterback Jason Campbell went 9-of-15 through the air for 141 yards.
Matt Forte rushed for 16 yards on four carries, while Michael Bush picked up 21 yards and two touchdowns on five carries.
Redskins rookie Kirk Cousins amassed 264 yards and three touchdown strikes on 18-of-23 passing.
Fellow rookie signal-caller Robert Griffin III, meanwhile, compiled 49 yards on 5-of-8 passing while playing the entire first half. He also gained 17 rushing yards.