Mirza took advantage of a rash of double faults from Kutuzova on her way to a 6-4, 6-3 win.
In the last eight tomorrow, Mirza will play Marion Bartoli of France, seeded second, who beat Japan’s Kurumi Nara 6-1, 6-1.
In other second-round action, fourth seed Francesca Schiavone of Italy had an unconvincing win over Taiwan’s Chan Yung-jan.
Schiavone, ranked 26th in the world, took the first set 6-3 before her 106th ranked opponent from Dongshih Township in Taichung County won the next set without losing a game.
However the Italian bounced back to take the deciding set 6-3.
Melinda Czink of Hungary beat Vania King of the US 6-4, 6-2.
ADDITIONAL REPORTING BY STAFF WRITER
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