The Indians won the high-quality match first round match 7-6 (5) 4-6 12-10 after battling hard for close to two hours.
The Chennai boys next face second seeded South African team of Dean O' Brien and Ruan Roelofse, who knocked out Americans Mitchell Krueger and Mackenzie McDonald 6-4 6-4 in their first round.
In the singles, Ramkumar is scheduled to play Australia's Whittington after getting the better of his compatriot Luke Saville 4-6 6-2 6-1 in his opening round.