The meeting lasted 1 hour 44 minutes and ended with a score of 7: 5, 6: 3 in favor of the 37-year-old athlete.
Zvonareva is a three-time doubles Grand Slam champion and a two-time major singles finalist.
In the next round, Zvonareva will face the ex-first racket of the world, Japanese Naomi Osaka, who defeated Frenchwoman Alize Cornet.
Earlier it was reported that tennis player Varvara Gracheva was devastatingly lost at the start of the Melbourne Summer Set 2 tournament in Melbourne.