The 2017 U.S. Open champion also lost to the unseeded Croat in the first round at Wimbledon.
Also, seventh-seeded Ashleigh Barty reached the second round by beating CoCo Vandeweghe 4-6, 6-3, 7-5, while No. 8 Barbora Strycova defeated Zarina Diyas 6-4, 6-4.
In other matches, Johanna Konta defeated Gabriela Dabrowski 6-2, 6-0, and Alison Riske beat Eugenie Bouchard 6-4, 6-4.
Caroline Wozniacki is the top-seeded player at the tournament and Caroline Garcia is No. 2. Both had byes in the first round.
Third-seeded Naomi Osaka, who won the U.S. Open just over a week ago, also had a bye and plays Wednesday against Dominika Cibulkova.
More AP tennis coverage: https://apnews.com/tag/apf-Tennis and https://twitter.com/AP_Sports