Top seed Wozniacki battled back from a 5-2 deficit in the second set to overcome American teenager Taylor Townsend 6-1 7-6, while Williams defeated Japan???s Kurumi Nama 6-4 6-1.
Wozniacki raced through the first set against Townsend, but the 2012 junior Australian Open champion found some rhythm in the second and won four successive games.
However, nerves got the better of Townsend as Wozniacki scrambled back to 5-4 before saving three set points to level at 5-5, and the former world No 1 won the tie-break 7-4 to a book a last-eight date with Germany???s Julia Goerges.
Third seed Williams, who spent less than an hour on court on Tuesday, took a little longer to overcome Nara.
The American edged a tight first set but dominated the second to set up a tricky quarter-final tie with Russia’s Elena Vesnina.
The Russian world No 64 4 has a 2-1 career record over Williams, including a sensational 6-1 6-3 victory over the American in the first round at Wimbledon in 2012.
“When I played her at Wimbledon it was very special,” said Vesnina. “I won that match in two sets and I was so happy because I didn’t expect it.
“She’s a super great player, but on grass she’s the best of the best and to beat her there was amazing and I’m always saying this is the biggest win of my career.
“I’ll go on the court and I’ll try to show my best tennis, I’ll try to play aggressively, move her around.
“Whenever you go on court you want to win the match no matter who you’re playing.”