In the first set the fifth seed broke Benneteau's serve on three occasions. The Frenchman had break-point chances to get back in it but could not take them.
Benneteau got on the board by holding his first service game of the second but was broken at the next opportunity, with Berdych holding his remaining service games to come through.
Berdych was not threatened in the third set and won the last nine points in a row to seal victory in under two hours.
Next up for the Czech is a match against 19th seed Stanislas Wawrinka, who overcame Marcos Baghdatis in a tough slog.