Leander and his Spanish partner Fernando Verdasco got the better of Germans Florian Mayer and Frank Moder 6-2 6-3 in the opening round of the men's doubles competition.
It took Paes and Verdasco just 62 minutes to advance as they saved two break chances and converted all the three breakpoints they earned.
They next face American giant-killers Steve Johnson and Sam Querrey, who knocked out top-seeded compatriots Mike and Bob Bryan 7-(4) 5-7 6-3.
In women's doubles, the top-seeded Indo-Swiss pair of Sania and Martina Hingis dispatched the Americans Kaitlyn Christian and Sabrina Santamaria 6-1 6-2 in the first round.
However, the hot favourites lost their service twice in the 56-minute contest in which they broke their rivals seven times.
They now face Swiss Timea Bacsinszky and her Taipei partner Chia-Jung Chuang, who defeated American team of Melanie Oudin and Jessica Pegula 6-4 7-6 (5).
Rohan Bopanna, who has already reached the men's doubles second round, will open his mixed doubles campaign tomorrow with his Tapiei partner Yung-Jan Chan. The second seeds face Belinda Bencic from Switzerland and Fernando Verdasco.
Sania will also begin her title defence with Brazilian partner Bruno Soares. They are up against Czech Republic's Andrea Hlavackova and Lukasz Kubot from Poland.