The 33 year-old won an all-Ukrainian contest against Kalinina 3-6 6-4 6-3 to set up a clash with Jule Niemeier after the German's upset of second seed Anett Kontaveit.
The pair were cheered on by flag-waving supporters at SW19, while Tsurenko sported a blue-and-yellow.
Tsurenko expressed her disappointment over the lack of vocal opposition from Russian and Belarusian athletes, who are banned from playing at the All England Club, to the war in Ukraine after she moved into round three.
"I would be the first one to say that, no, you should not ban them," she said. "But I have heard only from one Belarusian player and from one Russian player, who talked to me personally and told me: ‘I’m against the war.’
"I did not hear anything from any other player. So for me, the silence means … I mean, it's not good when … I don’t know. I thought I had a lot of friends on tour, especially from Russians and Belarusians.
"It’s just a step. [But] it's a good step to show that that's what we all have to do. I am Ukrainian. There is no other opinion in my head."