Third seeds Paes and his Czech partner Lukas Dlouhy toiled in the middle for nearly one-and-half hours before eking out a 6-4, 7-6(4) victory over Ross Hutchins and Jordan Kerr.
They now face the unseeded Thomaz Belucci-Marc Lopez pair who struggled to down the Christopher Kas-Dick Norman duo 3-6, 6-3, 10-8.
Bhupathi and Max Mirnyi also overcame a tricky test against 2005 Wimbledon champions Stephen Huss and Wesley Moodie before they carved out a 6-4, 7-5 victory in 76 minutes.
The fourth seeded Indo-Belarussian pair now face the John Isnor-Sam Querry duo, who toiled to get past Johan Branstrom and Jean-Jullen Rojer 4-6, 6-3, 10-7 in yet another intense opening round match.
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