Cepede Royg, ranked 97th, had a break point while leading 4-3 in the decider, but Pliskova overcame that scare and won the remaining games.
Pliskova, the 2016 U.S. Open runner-up, will take on Caroline Garcia of France for a place in the semi-finals.
Cepede Royg made an impressive start as she sprayed Court Suzanne Lenglen with winners but nerves eventually kicked in, allowing Pliskova to secure victory after one hour and 51 minutes.
(Reporting by Julien Pretot; Editing by Pritha Sarkar)
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