The 54th-ranked Tsurenko needed only 77 minutes to complete the second-round victory on the grandstand court.
The 21-year-old Muguruza has risen to No. 9 after her run to the final at Wimbledon. The Spanish player lost to Serena Williams for the title after beating four top-15 players at the All-England Club.
The top-ranked Williams will play her third-round match Thursday night.
Second-seeded Simona Halep of Romania and fifth-seeded Ana Ivanovic of Serbia also advanced to the third round, while third-seeded Petra Kvitova of the Czech Republic and fourth-seeded Caroline Wozniacki of Denmark dropped out.
Halep beat Jelena Jankovic of Serbia 6-3, 6-4; Ivanovic topped Belarus' Olga Govortsova 6-4, 7-6 (4); Belarus' Victoria Azarenka beat Kvitova 6-2, 6-3; and Switzerland's Belinda Bencic edged Wozniacki 7-5, 7-5.
Sixth-seeded Agnieszka Radwanska of Poland edged Germany's Julia Goerges 7-5, 6-3; Russia's Daria Gavrilova beat seventh-seeded Lucie Safarova of the Czech Republic 4-6, 7-5, 7-5; and Slovenia's Polona Hercog topped 11th-seeded Ekaterina Makarova of Russia 6-2, 6-7 (2), 7-5.