The world No 27 needed less than an hour to see off American Louisa Chirico 6-2 6-1 and, at one stage, reeled off eight games in a row.
The 20-year-old from Ukraine has spent the past two weeks training in high altitude ahead of this clay court event.
Her 18-year-old opponent – the world No 141 – did not help her cause by sending down six double faults.
In another match on Monday, two-time champion Lourdes Dom??nguez Lino of Spain beat the No 6 seed Shelby Rogers 6-3 6-2.
After making an early break, the American lost 11 of the last 14 games.