The 23-year-old Svitolina, who trains at Roland Garros and was a quarter-finalist in 2015 and 2017, had been tipped as one of the potential winners for the second year in a row after winning the Italian Open, but she never found her groove on Court One.
She dropped serve five times and made 29 unforced errors, bowing out on the first match point when she buried another forehand into the net.
Buzarnescu, who reached the final in Prague on clay last month, next faces American 13th seed Madison Keys, the 2017 U.S. Open runner-up.
(Reporting by Julien Pretot; Editing by Alison Williams)
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