Paes and his Czech partner Lukas Dlouhy were the first to take the court and the third seeds didn't have much trouble in sailing past Czechs Leos Friedl and David Skoch 6-3 6-1 in the first round of the men's doubles event.
Paes and Dlouhy will next take on Lucas Arnold Ker of Argentina and Romania's Horia Tecau.
But the newly-formed combination of Bhupathi and Belarusian Mirnyi disappointed with a 4-6, 4-6 loss to the unseeded German-Finnish pair of Michael Kohlmann and Jarkko Nieminen.
It was with Mirnyi that Bhupathi won his last Grand Slam men's doubles trophy when they triumphed at US Open in 2002.
Bhupathi ended his partnership with Bahamas' Mark Knowles after playing 2009 US Open.
However, 10th seeds Sania and her Spanish partner Virginia Ruano Pascual ensured that India ended the day on a high with a comfortable 6-4, 6-2 triumph over the unseeded Indonesian-Japanese duo of Yayuk Basuki and Kimiko Date Krumm.
Sania and Pascual will face Timea Bacsinszky of Switzerland and Tathiana Garbin of Italy in their second-round match.