The second-seeded Ivanovic, who lost in the French finals to the now-retired Justine Henin last year, moved on with a 6-2, 7-5 win over Sweden's Sofia Arvidsson despite committing 36 unforced errors.
Former French Open champion Williams, the No. 5 seed, eliminated fellow American Ashley Harkleroad 6-2, 6-1.
The 20-year-old Ivanovic said she let her "intensity go down a bit" against Arvidsson but "towards the end I'm happy that I found back my game ... ."
Others advancing included Czechs Iveta Benesova, Klara Zakopalova and Lucie Sararova, Alize Cornet, and Nathalia Dechy of France, Dominika Cibulkova of Slovakia, Carolina Wozniacki of Denmark, Anastasiya Yakimova of Belarusm, Russians Ekaterina Makarova and Galina Voscoboeva and Tunisia's Selima Sfar.
2014: The Year in Music [PHOTOS]