Vekic was on the court only 39 minutes in a 6-1, 6-0 victory over Nazrin Jafarova, a local player given a wild-card pass into the main draw. Vekic won three-quarters of the points in the match, including 80 percent -- 28-of-35 -- on serve.
She also won 21 of the 30 points off Jafarova's serve and cashed in five of her six break chances.
No. 4-seeded Alexandra Cadantu stopped Michaella Krajicek 2-6, 6-0, 6-3. She turned the match with a strong second set in which she took 12 of the 13 points when Krajicek served.
Tadeja Majeric ousted fifth-seeded Karolina Pliskova 7-5, 6-4 while losing her serve just once and wild-card entrant Ons Jabeur raced to a 6-4, 6-0 victory over Daria Gavrilova in 55 minutes.
Defending champion Bojana Jovanovski, the top seed this year, is to open her play Tuesday.