Sania Mirza too advanced into the quarterfinal of the mixed event partnering Briton Colin Fleming on Sunday.
It was also the end of road for Mahesh Bhupathi, who lost the first round of men's doubles with Rohan Bopanna, as he decided to pull out of the mixed doubles event with Andrea Hlavackova. The sixth seeded pair of Bhupathi and Hlavackova gave a walkover to unseeded Spanish duo of Nuria Llagostera Vives and David Marrero.
Hlavackova decided to concentrate on women's singles as she will take on former champion Serena Williams in the fourth round after defeating Russian 14th seed Maria Kirilenko.
Paes and his Czech partner Radek Stepanek eased through the third round of men's competition defeating America-Australian pair of Jesse Levine-Marinko Matosevic 6-1, 6-3.
The fifth seeds broke Levine-Matosevic four times without losing a single game in the match. Sixteen unforced errors by the unseeded pair also proved crucial for the losers as they gave away points at important junctures.
In the mixed doubles, third seeded Elena Vesnina of Russia and Paes faced a tough challenge from Americans Abigail Spears and Scott Lipsky but won 4-6, 6-4, 1-0(5) in one hour and 21 minutes
After exchanging the first two sets the Indo-Russian duo took away the tie-breaker with ease.
Mirza and Fleming drubbed the American pairing of Melanie Oudin and Jack Sock 6-4, 7-6 (7) in one hour and 25 minutes.
The Indo-British duo won the first set in 35 minutes. However, both teams held serve in the second set till the tie-breaker which Mirza-Fleming won 9-7 in a tough fight.
Sania, however, lost her women's doubles third round match partnering American Bethanie Mattek-Sands.
They went down to second seeded Italians Sara Errani and Roberta Vinci 6-4, 6-7(7), 6-3 in two hours and 16 minutes.
After losing the first, the Indo-American pair bounced back to level the match in the second set tie-breaker. However, the duo could not challenge the experienced second seeds and gave away the decider.