The win allows the Redskins (7-7) to maintain at least a share of the lead in the NFC East heading into a showdown next Saturday night in Philadelphia.
The New York Giants (6-8) lost to the Carolina Panthers on Sunday. The Eagles (6-7) host the Arizona Cardinals Sunday night.
Cousins threw for two first-half scores to Jordan Reed and ran one in from 13 yards to push the ‘Skins to a 21-0 lead at the half.
Buffalo (6-8) closed to within 28-17 on a 48-yard TD pass from Virginia Tech alum Tyrod Taylor to Sammy Watkins with 3:48 left in the third.
Cousins connected with Pierre Garcon on a 5-yard TD pass with 11:16 to go in the game to extend the lead to 35-17.
The Bills got another Taylor-to-Watkins TD, a 20-yard score, with 1:26 to go.
Cousins was 22-for-28 passing for 319 yards. Alfred Morris ran for 84 yards on 14 carries for Washington, which had DeSean Jackson catch six balls for 153 yards, including a 77-yard third-quarter touchdown.
Taylor was 16-for-27 passing for 235 yards and two touchdowns for the Bills, who rang up 240 yards on the ground on 31 rushes.