Svitolina will play either 17th-seeded Ekaterina Alexandrova or Britain's Heather Watson in the third round after a routine win over Zvonareva in just over an hour.
Third-seeded Aryna Sabalenka came from two breaks down in the deciding set to eliminate American teenager Coco Gauff 1-6, 7-5, 7-6 (2).
Halep, who lost the 2017 and 2018 Rome finals to Elina Svitolina, extended her record in tennis’ restart to 10-0.
Pliskova surged ahead of Anhelina Kalinina 4-1 in the opening set, lost three games in a row, then took the last eight for a 6-4, 6-0 victory. She had a 26-7 edge in winners
Pliskova, who has won 16 WTA tour titles in her career so far, is famous for her calm on-court demeanour as well as her big serving.
The event is scheduled to be played from May 26 to May 28 in the capital city of Czech Republic.
Anastasia Pavlyuchenkova defeated Karolina Pliskova 7-6, 7-6 to win her third round fixture and set up a clash with Angelique Kerber.
Serena Williams won her first title since 2017 on Sunday after she won the ASB Classic in Auckland.
The second-ranked Pliskova is the first player, male or female, to win the Brisbane-based event three times after wins here in 2017 and last year.
Barty, like Svitolina, dropped the opening set of her semifinal before beating second-ranked Karolina Pliskova of Czech Republic 4-6, 6-2, 6-3.
In the semifinals, Pliskova will take on top-ranked Ash Barty — Australia's first female year-end No. 1.
Simona Halep saved a match point before beating Bianca Andreescu 3-6, 7-6, 6-3 while Elina Svitolina defeated Karolina Pliskova 7-6, 6-4.
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