The American twins switched sides after dropping the first set then found themselves down a break in the second before rallying to beat Canadians Daniel Nestor and Vasek Pospisil 6-7(1) 7-5 6-2.
"It ended up working out but it was just a desperate call," said Bob Bryan.
"We were feeling a little bit hopeless on the return games, and throwing in a switch like that sometimes is a psychological advantage."
The Bryan brothers have already won each of the last four Grand Slam doubles titles, starting with last year's US Open, but are bidding to claim all four in the same calendar year.
The only men to have achieved the feat were the Australian pair of Ken McGregor and Frank Sedgman in 1951.