The sixth-seeded pair of Bhupathi and Bopanna defeated Argentine pair of Juan Monaco and Horacio Zeballos 6-3 3-6 10-5 in a hard-fough contest to make it to the last eight of the competition, which is considered to be warm-up event for the French Open.
However it was a disappointing day in office for Paes and his Austrian partner Jurgen Melzer.
The German-Czech combination of Tommy Haas and Radek Stepanek hardly broke sweat as they beat the Indo-Austrian combination in straight sets 7-5 6-1.
In the women's event, the fifth seeded pair of Sania and Bethanie Mattek-Sands of the United States were beaten by Anastasia Pavlyuchenkova and Lucie Safarova.
The Russian pair won by 7-5 6-1 margin. Bhupathi and Bopanna showed more consistency in their both first and service.
They won 76 percent points on their first serve compared to 68 percent of their opponents.
The Indian pair fared better in the second serve also as they won 67 percent points compared to only 50 percent by the Argentine pair.
In the end, the Indians prevailed as they pipped their opponents by 60 to 53 in the total points in the offing.
Leander and Melzer were off-colour today as Haas-Stepanek pair broke their service on four occasions which was testimony to the supremacy of the German-Czech duo.
In the total number of points, Haas-Stepanek won 58 percent while Paes-Mlezer could win only 42 percent of the points.