A.J. Green made nine catches for 183 yards, including a 73-yard TD pass tossed by fellow wide receiver Mohamed Sanu on the first play from scrimmage for the Bengals (2-1).
BenJarvus Green-Ellis gained 38 yards on 17 carries for Cincinnati.
Washington (1-2) dropped its second straight despite 221 passing yards from Robert Griffin III, who completed 21-of-34 attempts after a slow first half.
The rookie signal-caller also was the Redskins' leading rusher with 85 yards and a score.
N.J. man wakes up from 10-hour sleep with knife in back
Police: Sword-wielding man demanded free tacos