Tsurenko followed up her second-round win over Australia's Jarmila Gajdosova with a 6-3, 6-4 win over Slovakia's Daniela Hantuchova.
"I'm the first time in my life lucky loser, and it's really surprising for me to take the spot of Maria Sharapova,'' Tsurenko said. "I'm just enjoying now. That's my chance. I'm just taking it. "
In the men's second round, Grigor Dimitrov of Bulgaria upset No. 2-seeded Milos Raonic of Canada 6-3, 6-4.
Defending champion Andy Murray, the Olympic and US Open champion, was playing Australian qualifier John Millman in a night match.