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.
Scarlett Johansson steps out with fiance after pregnancy reveal
Teacher apologizes for showing sexual image of herself in class