The 19-year-old Croatian beat Williams 7-6 (7-5), 7-6 (8-6). It was the American's earliest exit at Wimbledon since 1997.
American Andy Roddick defeated 19-year-old Yeu-Tzuoo of Chinese Taipei 6-3, 7-5, 6-4 in the first round.
Guillermo Coria, of Argentina, finally overcame South African Wesley Moodie in a first-round match played over four days because of rain delays.
Other seeded winners included Australian Lleyton Hewitt, Juan Carlos Ferrero and Carlos Moya of Spain, German Rainer Schuettler, Tommy Rebredo of Spain, Dominik Hrbaty of Slovakia and Taylor Dent and Vincent Spadea of the United States.
Winners on the women's side included second-seeded Anastasia Myskina of Russia, No. 4 Amelie Mauresmo of France and fifth-seeded Lindsay Davenport and No. 7 Jennifer Capriati of the United states.
Celebrity Couples of 2014 [PHOTOS]