Washington went ahead 31-14 on Evan Royster’s 4-yard run.
Weeden came back with a 69-yard scoring strike to speedy rookie Travis Benjamin to pull the Browns within 10, but Cousins calmly took the Redskins down the field with Morris scoring to make it 38-21.
With Griffin out and inactive, Shanahan had to tweak his game plan and Cousins ran it with precision.
‘‘He was nervous and wanted to get out there so bad,’’ nine-year cornerback D'Angelo Hall said. ‘‘I told him to just go out and play, we have your back. We saw him win last week. We knew if he played a whole game he would do good things.
‘‘It’s good to see the car keys turned over to somebody else and we win.’’
Richardson’s second TD run gave the Browns a 14-10 lead with 1:11 left before halftime. Earlier, he broke Hall of Famer Jim Brown’s 55-year-old team rookie record for rushing TDs.
NOTES: Redskins K Kai Forbath made a 44-yard field goal and is 15 of 15, one shy of the NFL record to start a career. ... Morris has nine rushing TDs, passing Skip Hicks (1998) for the most by a Redskins rookie. ... Shanahan said OT Tyler Polumbus has a concussion. ... Shanahan did not have any updates on injuries to LB Lorenzo Alexander (shoulder) or OL Will Montgomery (knee).
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