Sania, seeded 21st, lost the first set via the tie-breaker, but managed to come back strong in a tightly-fought second set winning it 7-5. However, the world number 32 had an easy time in the decider as she clinched it 6-3 to seal the contest.
It was Sania's fourth victory in as many matches over Peer, her former doubles partner.
"I was a bit irritated with myself, because I was fighting, fighting, the whole time, coming back all the time, levelling up and then not going up or finishing it," Sania said after the match.
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