The 46th-ranked Ukrainian will next face fourth-seeded Czech Lucie Safarova, who came from a set down to scrape past Slovakia's Dominika Cibulkova 7(4) 6-4 7-5 in just under three hours.
"It was actually really relaxing for me because I was really disappointed with my loss in qualies," Tsurenko said courtside after her win against Pliskova, the world number eight.
"Then I got in and I felt this is probably my chance to show some good tennis and try some stuff for the U.S. Open (which starts on Monday).
"So I think it was a good chance for me to play good. I don't feel any pressure because I'm playing players who are higher ranked than me."
French Open finalist and world number six Safarova battled back from a break down in the final set to beat Cibulkova for only the second time in six career meetings.
"I was just fighting for each point because I know she's a big fighter, and my (head-to-head) score wasn't positive against her," Safarova said of her plucky win against the 58th-ranked Slovakian. "So I'm really happy to pull this out."
Second-seeded Czech Petra Kvitova blasted six aces past seventh seed Agnieszka Radwanska of Poland and broke her opponent's serve five times on the way to a 7-5 6-4 victory after one hour and 40 minutes.
Left-hander Kvitova will next meet either third-seeded Dane Caroline Wozniacki, a four-time Connecticut Open champion, or Caroline Garcia of France who were scheduled to play in Thursday's evening quarter-final.
(Reporting by Mark Lamport-Stokes in Los Angeles; Editing by Frank Pingue)
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