The unseeded Indian overcame world number 80 Edouard Roger-Vasselin from France 4-6 6-4 7-5 in the second round.
Somdev saved seven of the nine break chances he faced in the match and that proved crucial in his win.
With this victory, Somdev levelled the head-to-head record 1-1 with Edouard. The last they played was in 2009 when the Frenchman had emerged winner on Rhodes, Greece.
He now plays the six-time Grand Slam winner for a place in the quarter-finals. In his previous clashes with one of the greatest players of all time such as Rafael Nadal, Somdev had put up a good challenge.
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Bhupathi and Nestor notched up a 7-6 (3), 6-3 win over their French opponents in a 79-minute opening round match.
The third-seeded Indo-Canadian pair came from behind to force a tie-break in the first-set but they were in control of the second set. Bhupathi and Nestor won 82 per cent of their service points and saved both the break points they faced.
They next play Spaniard Nicolas Almagro and his Austrian partner Oliver Marach, who beat Colombian Juan Sebastian Cabal and his Mexican partner Santiago Gonzalez 6-3, 6-4, in their first round match.