Bhambri, ranked 195th in the world, built a 6-1, 5-5 lead over third-seeded Fabio Fognini when Fognini was unable to continue the match due to a leg injury. Bhambri finished off both of his break chances in the first set and another in the second in advancing.
No. 4-seeded Benoit Paire rolled past Guillermo Garcia-Lopez 6-1, 6-4 by saving 11 of the 12 break points he faced. On the other side, Paire was able to convert four of his own six break chances.
Sixth-seeded Marcel Granollers moved into the quarterfinals with five breaks over a 6-2, 6-4 victory over Ramkumar Ramanathan. Granollers ended up winning nearly 60 percent of the points in the match.
Vasek Pospisil, the No. 5 seed, also made it through to the quarterfinals, advancing when Lu Yen-Hsun was unable to play Thursday.
Pospisil and Paire are to meet in Friday's quarterfinals with a match between Dudi Sela and Edouard Roger-Vasselin also in their half of the draw. The quarters in the top half of the draw see Bhambri going against Pospisil and top-seeded Stanislas Wawrinka taking on Aljaz Bedene.