One of the best sprinters in the field, O'Grady was too strong for Hincapie and easily beat him on the finish line after the 149 kilometres ride between Bollène and Sisteron, in the foothills of the Alps.
Both riders were credited with a time of three hours 13 minutes 21 seconds.
O'Grady and Lance Armstrong's team mate Hincapie had broken away with six other riders after 55 km of the stage and the pair parted company with the leading group 55 km later.
Australian Baden Cooke finished third, one minute and 33 seconds back, while the peleton, with Spanish overall leader Iban Mayo and Armstrong, crossed the line 6:12 behind O'Grady.
Mayo retained his race leader's jersey with a 36 second lead over American Tyler Hamilton, while Armstrong remained fourth, exactly two minutes behind the Basque rider.