McCluster's play early in the second quarter amid snowy conditions at FedEx Field gave the Chiefs 31-0 lead and Kansas City went on to easily break a three-game losing streak.
Quintin Demps returned a kickoff for a score and Alex Smith supplied a pair of TD passes for the Chiefs (10-3).
Jamaal Charles piled up 151 rushing yards rushing with a score on 19 carries and also grabbed a scoring pass.
The Redskins (3-10) slumped to a fifth straight loss as Robert Griffin III was held to 164 passing yards with a score on 12-of-26 efficiency.
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