Sharan and American Ram faced stiff resistance from Fabio Fognini and Marcel Granollers before winning 4-6 7-6 (7-4) 6-2 in the second round which lasted for two hours and eight minutes.
The left-handed Sharan's serve came under pressure in the tight second set but he was excellent at the net, producing some quality volleys.
Last year Sharan had made the third round at the French Open with Purav Raja. He had also reched the US Open third round in 2013.
They are now up against seventh seeds Mate Pavic of Croatia and Austria's Oliver Marach who edged out Artem Sitak and Wesley Koolhof 6-7 (5) 6-4 6-4.
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