ReutersThe fourth seeds, who were runners-up at the 2012 Australian Open, claimed their first Grand Slam doubles title.
Vinci and Errani have also won tournaments this year in Monterrey, Acapulco, Barcelona, Madrid and Rome.
Errani, who plays Maria Sharapova in the singles final on Saturday, is the first player since Kim Clijsters in 2003 to reach the singles and doubles finals at Roland Garros in the same year.
She is hoping to emulate Mary Pierce who was the last woman to win both titles at the French Open in 2000.
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