The Czech seemed to have everything under control after recovering from the loss of the first set but her game went off the boil and Sabalenka stormed back to win 6-3 2-6 7-6(5).
Sabalenka's first victory over a top-10 opponent means that in the semi-finals she will face former champion Agnieszka Radwanska, who got the better of Latvian Jelena Ostapenko.
After dropping serve at the start of the decider, Pliskova reeled off four games as Sabalenka's hopes faded.
But Sabalenka regrouped, ground her way back to parity and got herself into a tiebreak.
At 5-5 it seemed seventh-ranked Pliskova's greater experience would prevail but Sabalenka crunched a backhand winner to reach match point and could celebrate when her opponent fired a forehand wide.
Radwanska, who received a walkover when twice-Wimbledon-champion Petra Kvitova withdrew on Wednesday, said she was surprised to still be involved after a 6-2 7-5 win.
"I took only three dresses with me - (I thought) it's enough for sure," said Radwanska, sidelined since April with back and hip injuries.
"I thought maybe one or two matches at the most - especially as I'm unseeded."
World number two and top seed Caroline Wozniacki, runner-up at the south coast event last year, cruised into the semi-finals with a 6-4 6-3 win over Australia's Ashleigh Barty.
Denmark's Australian Open winner will next meet Angelique Kerber, the double grand slam champion who had to battle from 3-1 down in the final set tiebreak before beating Russia's Daria Kastkina 6-1 6-7(3)7-6(3) in the best match of the day.
In the men's event, surprise French Open semi-finalist Marco Cecchinato of Italy reached the last four with a 5-7 6-3 6-2 defeat of Australian John Millman.
He will face Slovakia's Lukas Lacko, who ended the hopes of British wild card Cameron Norrie.
Canadian third seed Denis Shapovalov was knocked out by Mischa Zverev although the result was not a total surprise given the German's natural grasscourt game.
Zverev will face Kazakhstan's Mikhail Kukushkin, who defeated home hope Kyle Edmund 5-7 6-3 6-1, in the semis.
(Reporting by Martyn Herman and Ian Chadband; Editing by Catherine Evans)
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