The world number one overcame Belgium's Kim Clijsters 6-4 6-4 to set up the prospect of a compelling clash with Williams, the fifth seed who overpowered fellow American Brie Rippner 6-1 6-2.
Australian Open champion Lindsay Davenport and last year's Sydney international winner Amelie Mauresmo also moved through to the last eight but seeds Anna Kournikova, Amanda Coetzer and Jennifer Capriati all bowed out.
Arnaud Clement of France made an early exit from the men's draw when he was beaten by George Bastl and last week's Australian hardcourt champion Tommy Haas fell to fellow- German Rainer Schuttler 7-6 7-6 in a match that finished after midnight.
But the remaining big names, including top seed Magnus Norman and defending champion Lleyton Hewitt, all won.
Hingis teamed up with Monica Seles to beat Serena and Venus Williams in an epic centre-court doubles match on Tuesday but the effort drained her and she was clearly tired against the improving Klijsters.
Hingis struggled through the first set and was in trouble in the second set when she was sparked into action after being warned for coaching as her mother screamed instructions at her from the sideline.
Hingis quickly seized the initiative and went on to win but said she would have to play better against Serena.
"I didn't play up to my best today but I was lucky it was good enough," Hingis said.
"It's always good to have tough matches before you play a big one so you know where you're at."
Serena hardly raised a sweat against Rippner and said she had plenty in reserve for the match with Hingis.
"I didn't have any problems," Williams said. "I'm like the Energizer battery, I keep going and going and going."
Davenport began her preparations for the defence of her Australian Open crown with a 6-3 6-3 win over Barbara Schett to set up a meeting with her old doubles partner Lisa Raymond, who defeated eighth-seed Capriati 2-6 6-3 7-5.
The winner of that match meets either Seles or Mauresmo in the semifinals. Seles won her second-round match on Tuesday while the unseded Mauresmo joined her in the last eight when she overpowered seventh-seed Coetzer 7-5 7-5.
American Corina Morariu eliminated sixth-seed Kournikova 6-1 6-2 to secure a quarter-final meeting with French Open finalist Conchita Martinez.
"Obviously to beat such a good player with such an easy score is a bit of a surprise, but I went into the match pretty confident," Morariu said.
Norman eased past Australia's Todd Woodbridge 6-3 6-1 to advance to a quarter-final meeting with Bastl after the Swiss qualifier beat Clement 5-7 6-2 6-2.
Defending champion Hewitt also cruised through after a 6-4 6-1 win over fellow Australian Andrew Ilie.