Tsurenko, a finalist at the Brisbane International two weeks ago, had only nine winners in the 54-minute match.
The 17-year-old Anisimova, born in New Jersey to Russian-born parents, is ranked 92nd and is the youngest of all players currently ranked in the Top 100.
Kickoff each day of the 2019 Australian Open with Tennis Channel Live, reviewing the day's most important news and previewing the day's biggest matches. Watch LIVE at 6 p.m. ET.
Follow the Australian Open even closer with Tennis Channel PLUS. Go to BuyTCPlus.com and subscribe now!