Cleveland quarterback Grandon Weeden went 10-of-13 for 112 yards without an interception during the exhibition opener and hit Dion Lewis with a 2-yard scoring pass 4 seconds into the second quarter.
The Browns held the Rams on their next possession and Benjamin went the distance on the ensuing punt return for a 17-0 lead.
Sam Bradford completed 5-of-8 passes for the Rams and found Chris Givens with a 3-yard scoring toss in the second period.
The Rams' Greg Zuerlein, who was good on 7-of-13 field goal attempts from beyond 50 yards in his rookie season of 2012, hit kicks of 55 and 54 yards.
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