Capriati, who received a first-round bye, became the second women's top seed in four years to lose her opening match here when she fell, 7-6 (7-5), 3-6, 6-4. She sustained a hip flexor during the second set and underwent treatment in the third.
With the withdrawal of world No. 1 Lindsay Davenport, Capriati is the top seed at next week's Australian Open, where she won her first career major.
Stevenson, a qualifier, defeated her first top five player and reached the quarterfinals of an event for the first time since this tournament two years ago.
Fourth seed Serena Williams of the United States, meanwhile, became the first player to reach the semifinals when she topped sixth seed and 2000 champion Amelie Mauresmo (6), 6-4, 7-6 (8-6).
The rest of the second round followed form as third-seeded Kim Clijsters of Belgium rallied past Silvia Farina Elia of Italy, 6-7 (4-7), 6-4, 6-1; fifth seed Justine Henin of Belgium ditched Conchita Martinez of Spain, 6-0, 6-3; No. 7 Sandrine Testud of France routed Henrieta Nagyova of Slovakia, 6-1, 6-2; and No. 8
In men's second-round action, second seed Roger Federer of Switzerland eased by Xavier Malisse of Belgium, 6-2, 6-4, and third-seeded Andy Roddick of the United States posted a 6-0, 6-4 victory over Bohdan Ulihrach of the Czech Republic.
Federer will take on Chile's Marcelo Rios, a 6-1, 6-4 winner over Romanian Andrei Pavel, 6-1, 6-4, while Roddick will battle Hyung-Taik Lee of Korea. Lee routed 1998 champion Karol Kucera, 6-1, 6-2.
Just two seeds remain after Nicolas Escude, who was instrumental in France's Davis Cup victory over Australia in last month's final, ousted No. 4 Guillermo Canas of Argentina, 6-4, 6-1.
Escude will play Juan Ignacio Chela of Argentina, who outlasted fellow qualifier Wayne Ferreira of South Africa, 6-4, 1-6, 7-6 (7-1).
The impressive run of Paradown Srichaphan of Thailand came to an end. After reaching his first career ATP final last week in India, Srichaphan ousted top seed Sebastien Grosjean in the first round here. But he was handled easily by Max Mirnyi of Belarus, 6-2, 6-3, on Wednesday.
Mirnyi's quarterfinal foe will be France's Juilen Boutter, who got past Rainer Schuettler of Germany, 6-4, 7-6 (7-3).
Celebrity Families of 2014 [PHOTOS]