Reigning Wimbledon champion Kerber beat Swede Rebecca Peterson 7-6(4) 6-0 and Pliskova crushed Elise Mertens 6-1 6-2, although Halep was pushed hard by Polona Hercog before emerging with a 6-1 4-6 6-3 victory.
In a repeat of last year's final, Wozniacki lost 2-6 6-4 7-6(5) in a fierce battle with Sabalenka who fought back from 5-2 down in the third set, saving a match point, on the way.
Sabalenka crunched 40 winners to Wozniacki's 21 as she claimed a first win against a top-20 player this year, avenging last year's loss in the Devonshire Park final.
She will face third seed Kiki Bertens of the Netherlands next after she bet Anna-Lena Friedsam in straight sets.
German let-hander Kerber continued to thrive on the grass after a tricky claycourt season as she blazed past Peterson following a tough first set.
The fourth seed saved two set points in the opener but eased through the second with a dominant display.
"I'm feeling good so far," Kerber told reporters.
"The first set was really close and tough. Then I started good in the second set and finding then my rhythm even better in the second set, so it was a good match."
She will face Halep next after the Romanian was made to work hard by the powerful Hercog.
Pliskova, who reached the Eastbourne final in 2016 and 2017, was brutal against Mertens with her power game in full flow.
"I felt like, it's bad to say, but there was no chance that I was going to lose today," she said. "I just felt super confident after I made the quick break in the first set."
Jelena Ostapenko, a semi-finalist at last year's Wimbledon, suffered an injury scare as she retired in her match against Ekaterina Alexandrova who moves on to play Pliskova.
There was an upset, however, as local favourite Johanna Konta was beaten 6-3 6-2 by Tunisia's Ons Jabeur.
Unseeded Jabeur was far too tricky for world number 19 Konta as she reached her first quarter-final of the year.
She will play France's Alize Cornet for a place in the semis after she comfortably beat Zhang Shuai of China.
(Reporting by Martyn Herman, editing by Ed Osmond)
