But the Indian-Czech duo, who were losing finalists at the US Open, levelled the contest after a single break in the second set and took the match tie-break 10/5.
Seventh seeds Bhupathi and Bopanna were in eighth and last spot in the chase for a place at the season-ending finale in the most recent rankings.
Indian veteran Paes, 39, said he was at the stage of his career when he was "playing for milestones, playing for history".
"We've had a great year. It started off with a big bang. To do well early in a partnership is something that can happen," said Paes, whose victory at the Australian Open meant he had completed the full set of Grand Slam titles during his career.
"But to continue playing well right through the whole year shows the quality of tennis that we play. For me personally what I really like about playing with Radek is we're looking to improve all the time. For me that's the potency of what the other guys feel.Djokovic triumphs
Novak Djokovic gained sweet revenge for his US Open defeat to Andy Murray on Sunday, saving five match points to seal a stunning 5-7, 7-6 (13/11), 6-3 victory in the Shanghai Masters final.