The sixth seeds lost 2-6, 6-3, 4-6.
Sania and Cara failed to cash in on a 4-1 lead in the third set and bowed out after an intense battle that lasted an hour and 48 minutes.
The top seeds will take on Kveta Peschke and Katarina Srebotnik (Czech Republic/Slovenia), who beat Jarmila Gajdosova and Ajla Tomljanovic (Australia/Croatia) 7-5, 4-6, 6-4, in the semi-finals.
The Indo-Zimbabwean won 81 points as against 89 by the Italians, but committed as many as 24 unforced errors, which, in the final analysis, proved costly.
Errani-Vinci won the opening set comfortably, converting three of the five break-points they got, while saving one of the two Sania-Cara forced.
But Sania-Cara came back strongly in the second set, scoring 11 winners against eight by the Italians. They also converted three of the five break-points they forced to take the game to the decider.
In the final set, they raced to a 4-1 lead, but just when they appeared well-set to clinch it, the top seeds reeled of the next three games to draw abreast at 4-4, saving six of eight break points, and proceed to take the set and match at 6-4.
Meanwhile, in the juniors girls’ doubles the Indian combo of Snehadevi Reddy and Dhruthi Tatachar Venugopal lost to top seeds Anhelina Kalinina of Ukraine and Russia's Elizaveta Kulichkova 1-6, 2-6.
Results (quarter-finals):
4-Kveta Peschke/Katarina Srebotnik (Czech Republic/Slovenia) beat Jarmila Gajdosova/Ajla Tomljanovic (Australia/Croatia) 7-5, 4-6, 6-4; 1-Sara Errani/Roberta Vinci (Italy) beat 6-Cara Black/Sania Mirza (Zimbabwe/India) 6-2, 3-6, 6-4; 3-Ekaterina Makarova/Elena Vesnina (Russia) beat 7-Andrea Hlavackova/Lucie Safarova (Czech Republic) 6-2, 2-6, 7-6(4); 8-Raquel Kops-Jones/Abigail Spears (US) beat Shahar Peer/Silvia Soler Espinosa (Israel/Spain) 6-4, 6-0.
Image: Sara Errani and Roberta Vinci of Italy in action during their fourth round doubles match against India's Sania Mirza and Cara Black of Zimbabwe
Photograph: Matt King/Getty Images
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