The two teams took one point each, confirming a top-two finish for table-toppers Kolkata
The veteran duo demolished Bruno Soares and Marcelo Melo in straight sets to extend their unbeaten streak in the tournament to 24 matches, the most by any doubles team in the world.
Paes and Bhupathi won 6-4, 7-6 (7/5), 6-1 in two hours and 19 minutes in front of some 2,000 home fans at the Nungambakkam Tennis Stadium in Chennai.
Brazil lead the tie 2-1 after hard-fought victories in Friday’s singles.
World number 27 Thomaz Bellucci beat the 479th-ranked Rohan Bopanna 6-7 (2/7), 7-6 (9/7), 7-5, 4-6, 10-8 in four hours and 28 minutes in the opening singles.
Ricardo Mello then marked his return to Davis Cup play after three years to oust India’s number one Somdev Devvarman 4-6, 6-2, 6-7 (3/7), 6-2, 6-4 in another classic that lasted four hours and 12 minutes.
Brazil, who have lost four consecutive play-off ties since 2006, need a win in one of Sunday’s two reverse singles to return to the World Group for the first time since 2003.
Bellucci takes on Devvarman in the first match, before Mello clashes with Bopanna.
India were forced into the play-offs after losing to Russia in the first round of the World Group in Moscow in March.
Paes, 37, and Bhupathi, 36, who won three Grand Slam doubles titles together before parting ways in 2001, team up for India in multi-nation events like the Olympics, Asian Games and the Davis Cup.
The two teams took one point each, confirming a top-two finish for table-toppers Kolkata
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