Williams, a two-time champion of the event, trailed Garbine Muguruza before retiring due to a viral illness.
Halep and Svitolina were impressive in third-round victories on Monday (AEDT), while Australian Ashleigh Barty also progressed.
Halep, the 2015 champion, was challenged but got past qualifier Kateryna Kozlova 7-6 (7-3) 7-5.
The Romanian was one of six seeds to progress, with Svitolina joining her after a 7-5 6-4 win over Daria Gavrilova.
Barty, the Australian 12th seed, was in fine form as she brushed past wildcard Jennifer Brady 6-3 6-2, setting up a meeting with Svitolina.
However, there was no such luck for the likes of Johanna Konta and Jelena Ostapenko.