Wimbledon champion, Angelique Kerber suffered a shocking 6-4 6-2 defeat to world number 81 Anastasia Potapova on Sunday.
Kudermetova will now face Kazakh world number 99 Zarina Diyas or France’s Audrey Albie, ranked 289th, in the second round after beating Wozniacki in the first round.
Meanwhile, Dutch fourth seed Kiki Bertens comfortably defeated French world number 66 Pauline Parmentier 6-3 6-4 on Suzanne-Lenglen.
And Australian Open quarter-finalist Ashleigh Barty, seeded eighth, beat American world number 72 Jessica Pegula 6-3 6-3.
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