Defending champions in mixed doubles, Paes and Swiss Martina Hingis prevailed over USA's Sachia Vickery and Frances Tiafoe 6-3, 6-2 in just 51 minutes.
They will take on the winner of the match between Anastasia Rodionova of Australia and Juan Sebastian Cabal of Colombia and seventh seeded American pair of Coco Vandeweghe and Rajeev Ram.
In Women's Doubles, seventh seeded Sania and her Czech partner Barbora Strycova defeated American pair of Jada Myii Hart and Ena Shibahara 6-3, 6-2 in an hour and nine minutes first round match.
The duo will meet the winner of the match between Swiss Viktorija Golubic and USA's Nicole Melichar and US-German combo of Madison Brengle and Tatjana Maria.
Men's Doubles pair of Rohan Bopanna and Frederik Nielsen of Denmark also reached the second round with a hard-fought 6-3, 6-7(3), 6-3 win over 16th seeds Radek Stepanek of Czech Republic and Serbian Nenad Zimonjic.
The Indo-Dane pair will square off against USA's Brian Baker and New Zealand's Marcus Daniell next.