Wozniacki, a former world No. 1 who has dropped to 11th in the rankings, raced past Arantxa Rus 6-1, 6-2 in 63 minutes. Wozniacki took nearly three quarters of the points on serve and saved all three break points she faced. She also finished off all four of her break opportunities.
Kanepi routed Han Sung-hee 6-1, 6-0 in 59 minutes. Kanepi took two-thirds of the points in the match, including 62 percent when receiving serve. She had five breaks in Han's six service games.
They were two of five seeded players to advance with wins Tuesday. The lone exception was fifth-seeded Julia Goerges, who fell to Silvia Soler-Espinosa 1-6, 7-6 (7-5), 6-2. Each player had five breaks but Soler-Espinosa had three in the final set in claiming the win.
Sixth-seeded Varvara Lepchenko stopped Camila Giorgi 6-2, 7-6 (7-1); No. 7 Klara Zakopalova edged past Garbine Muguruza 6-4, 4-6, 7-6 (7-1); and eighth-seeded Ekaterina Makarova defeated Polona Hercog 6-4, 6-1.
Unseeded winners Tuesday were Carolina Garcia, Magdalena Rybarikova, Jamie Hampton, Kiki Bertens, Galina Voskoboeva and Anabel Medina Garrigues.