Veteran Paes and Raja thrashed Serbia's Janko Tipsarevic and Viktor Troicki 6-1, 6-3 at the Flushing Meadows.
The 10th seeded combine of Bopanna and Uruguay's Pablo Cuevas, meanwhile, squandered a one-set advantage to go down to the former Australian Open winners Fabio Fognini and Simone Bolelli, 5-7, 6-4, 6-4 in an hour and 47 minutes in the men's doubles second round match.
Sania and her mixed doubles partner Ivan Dodig of Croatia lost to the Latvian-French pair of Jelena Ostapenko and Fabrice Martin 7-5, 3-6, 6-10.
Both are, however, still in the tournament - Bopanna will play the first of his mixed doubles match with Canadian Gabriela Dabrowski and Sania and her Chinese partner Peng Shuai will look to advance to the second round of women's doubles.
Divij Sharan who was paired up with No. 66 Andre Begemann lost 4-6, 4-6 to Spaniards Feliciano Lopez and Marc Lopez.
Paes and Raja's build-up to the tournament was far from ideal as they succumbed to an opening round defeat at the Winston-Salem Open.
However, the Indian duo bounced back in style at the US Open, converting 40 percent of their break points while conceding none.
Paes and Raja next face the Russian team of Karen Khachanov and Andrey Rublev.
Image: Leander Paes.
Photograph: Michael Dodge/Getty Images
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