Naomi Osaka was due to meet Madrid Open champion and sixth seed Kiki Bertens for a place in the final four of Italian Open.
Roger Federer admitted he struggled to get past the talented Gael Monfils.
Kiki Bertens fired eight aces to prevail 7-6 (7/2), 6-4 in one hour 43 minutes to record her first ever win over Donna Vekic.
Svitolina has looked on a mission at the WTA Finals in an effort to make amends for a lackluster early exit last year.
Naomi Osaka's WTA Finals debut ended in tears on Friday as she was forced to retire against Kiki Bertens.
By virtue of this win, Kiki Bertens secured her third WTA Tour singles title of the season.
Kiki Bertens defeated the world number one Simona Halep 2-6, 7-6 (8/6), 6-2 in the Cincinnati WTA final.
Kiki Bertens, who reached the French Open semi-finals in 2016, had never before been past the Wimbledon third round.
Petra Kvitova, the defending champion, dropped just one point on serve and stormed past Kiki Bertens into the second round.