It seemed Pliskova was on course to reach the semi-finals of the grass-court event that acts as a warm-up for Wimbledon but surrendered her advantage against 20-year-old Belarusian Aryna Sabalenka to lose 6-3, 2-6, 7-6 (7/5).
Sabalenka will now meet 2008 champion Agnieszka Radwanska in the last four.
The Pole, continuing her return from a back injury, defeated Jelena Ostapenko 6-2, 7-5.
Meanwhile, top seed Caroline Wozniacki, the 2009 champion and last year's beaten finalist, will face Angelique Kerber in Friday's other semi-final.
World number two Wozniacki, the Australian Open champion, beat eighth seed Ashleigh Barty 6-4 6-3, while Kerber had a much tougher time before seeing off Russia's Daria Kasatkina 6-1, 6-7 (3/7), 7-6 (7/3).
In the men's event, British number one Kyle Edmund was unable to build on his win over compatriot Andy Murray.
Despite winning the first set, Edmund lost 5-7, 6-3, 6-1 to world number 90 Mikhail Kukushkin.
Two-time Wimbledon champion Murray is returning from a longstanding hip injury, with the Scot set to announce on Friday if he will compete in this year's edition.
COMMENTS
Comments are moderated and generally will be posted if they are on-topic and not abusive.
For more information, please see our Comments FAQ