The 26-year-old needed one hour and 39 minutes to beat Pliskova, a former world No 1 who was the last Top 10 player left in this year's edition of the tournament, reported Efe.
Bertens is set to take on world No 13 Julia Goerges of Germany, who beat world No 55 Donna Vekic of Croatia 6-3, 6-2.
Latvia's Jelena Ostapenko also advanced to the last eight stage after she defeated Aliaksandra Sasnovich of Belarus 7-6 (7-4), 6-0.
Ostapenko took one hour and 18 minutes to move a step closer to winning her second Grand Slam title, having won the 2017 French Open.
The 21-year-old struck two aces and 28 winners compared to her rival's four and 14, respectively, and has yet to lose a set at Wimbledon this year.
In the upcoming round, Ostapenko will play Dominika Cibulkova of Slovakia, world No 33, who eliminated Taiwan's Hsieh Su-wei 6-4, 6-1.
Italy's Camila Giorgi, world No 52, staged her own upset over world No 35 Ekaterina Makarova of Russia 6-3, 6-4 in one hour and 30 minutes.
Up next, Giorgi is to square off against either 25th-seed Serena Williams of the US, or world No 120 Evgeniya Rodina of Russia.
(This story has not been edited by Social News XYZ staff and is auto-generated from a syndicated feed.)
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