Leander Paes and Elena Vesnina made a smooth progress to the mixed doubles quarter-finals of the French Open with a 6-2, 6-0 drubbing of Mathilde Johansson and Marc Gicquel, here, while Mahesh Bhupathi and Sania Mirza advanced to the QF after notching up a straight-set victory over unseeded opponents from France, Virginie Razzano and Nicolas Devilder, 7-6, 6-3 in a contest lasting an hour and 20 minutes.