Sevastova, who endured tough three-setters in the previous two rounds, kept alive her hopes of breaking into the world's top 10 for the first time with another determined display against former world number two Zvonareva.
"I think it was a great match. We played at a high level, she started on fire -- it was tough but I fought my way through," world number 11 Sevastova said.
The 28-year-old broke Zvonareva midway through the first set to take a 4-3 lead but the experienced Russian, who dominated the exchanges at the net, reeled off the next three games.
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After edging a tight second set with some big serves and powerful hitting, Sevastova switched gears from 3-3 in the decider to close out the victory.
Up next for Sevastova is qualifier Ons Jabeur who thumped Anett Kontaveit 7-5 6-1 to become the first Tunisian player to reach the semi-finals of a WTA tournament.
Briton Johanna Konta fought her way into the second semi-final of a patchy season with a 6-2 2-6 7-6(2) win over world number 31 Aliaksandra Sasnovich.
Konta, who has fallen to 44 in the rankings, next takes on Russia's Daria Kasatkina who came back from a break down in each set to beat compatriot Anastasia Pavlyuchenkova 6-4 6-3.
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