Benson's 4-yard TD with 9:14 remaining put Cincinnati ahead 20-6 and assured the result for the Bengals (8-6), who broke a two-game losing skid.
Cincinnati came into the contest one game behind the New York Jets for last AFC playoff berth.
Andy Dalton went 15-of-26 through the air for 179 yards with one interception for Cincinnati.
But the Rams (2-12) could get no closer and went down to their fifth straight loss.
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