Rovers were threatening to pull off a shock victory against the promotion-chasing hosts when Wayne Brown fired them ahead just after the hour mark.
Brown collected Ben Swallow's pass 20 yards out and rifled the ball past Addicks keeper Rob Elliot.
But Benson grabbed his seventh goal since joining Charlton from Dagenham when he tucked away a cross from Kyel Reid with 14 minutes remaining.
In a thrilling finish, the Addicks were denied a winner when Lee Martin fired narrowly wide and Mikkel Andersen saved from Alan McCormack and Akpo Sodje.
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