The Williams sisters had not dropped a set in this year's Championships and were back on court after Venus had earlier beaten Serena to retain the women's singles title.
They dominated after the early break and wrapped up the first set quite easily.
They failed to press home their advantage in the third game of the second set, when Raymond and Stosur clawed them back from 15-40 to deuce before going on to hold serve, but it was only a temporary reprieve.
They broke again at the next opportunity, after Stosur's first double faults of the match, and never looked back, wrapping up victory in just 59 minutes before a healthy number of spectators.
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