The seventh seeded Indo-American pair lost 1-6, 4-6 in just 66 minutes, losing serve three times in each set. Sania and Bethanie started the proceedings on an attacking note, breaking the serve of their opponents but the Italian pair of Errani and Vinci restored parity by breaking in the next game.
The top seeds Italian pair did not give Sania and Bethanie any more leeway to make a comeback into the match as they produced a dominant show to race through the set in just 24 minutes.
In the second set, the Indo-American duo took the first game at love but the top seeds put on display their vast repertoire of stroke-play to make a strong comeback.
The third game saw Sania-Bethanie saving three break points from 15-40 to surge ahead and then went on to win the next game to swell their lead to 3-1. However, their joy remained short-lived as the Italian duo of Errani and Vinci broke their opponents' serve to reduced the gap to 2-3.
Sania-Bethanie again made headway by breaking their opponents in the sixth game to take a 4-2 lead.
But, that was the last time luck smiled upon the Indo-American pair as Errani and Vinci won the next four games to book their berth semifinal berth in the championship.
They will meet the pair of Lisa Raymond and Laura Robson in the last-four. Sania and Bethanie had yesterday defeated the pair of Jarmila Gajdosova and Sabine Lisicki in the second round to make the quarters of the event.