The defeat means that Bhupathi and Belarusian Mirnyi will have to wait for their first title together since Rome event in 2004.
Bhupathi and Mirnyi had lost the Mimai Masters final to Leander Paes and Lukas Dlouhy and Monte-Carlo final to Nenad Zimonjic and Daniel Nestor.
The fourth seeds were up 2-0 in the opening set but Bryan brothers fought back strongly to win the next five games to securing a one-set lead.
The Americans then broke the second-set deadlock in the seventh game with a break of Bhupathi's serve and went on to claim victory and their eight title of the season in just under an hour.
Bhupathi and Mirnyi split USD 69,250 and earned 600 ranking points each for ending runners-up.
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