Former Grand Slam champions Azarenka, Rybakina into Brisbane semis
Azarenka took 2hr 30min before finally outlasting third-seeded Latvian Jelena Ostapenko 6-3, 3-6, 7-5 in the first match on Pat Rafter Arena.
The Brisbane tournament is a warm-up for the Australian Open, which the 34-year-old Azarenka won in 2012 and 2013.
Kazakhstan's Rybakina was then handed a spot in the last four when her Russian opponent Anastasia Potapova withdrew with a stomach problem after losing the first set 6-1.
Azarenka was in control early as she took the first set with one break of serve, but as the match progressed Ostapenko began to find her range and deservedly levelled.
Ostapenko, the 2017 French Open champion, was comfortable on serve in the third set while Azarenka struggled to hold hers.
But at 5-6 and serving to send the set into a tiebreak, the Latvian cracked and a poor service game handed the Belarusian victory.
Azarenka will play top seed Aryna Sabalenka or Daria Kasatkina in the last four.
"I thought the quality of tennis was incredible," Azarenka said. "She was blasting returns, blasting winners, so I had to stick in there.
"I was looking forward to seeing how my game was going to match up this year, and I think it's pretty good."
In another quarter-final, Rybakina raced to a 4-1 lead when Potapova asked for the trainer to treat what appeared to be a stomach injury.
She played the next two games but withdrew when 2022 Wimbledon champion Rybakina took the first set.
Rybakina will face Linda Noskova next after the Czech player saw off 16-year-old Russian Mirra Andreeva 7-5, 6-3.
In the men's draw, top seeded Dane Holger Rune looked in great touch as he downed Australian qualifier James Duckworth 6-2, 7-6 (8/6).
The world number eight will play Roman Safiullin in the semi-finals after the unseeded Russian beat Italy's Matteo Arnaldi 7-6 (7/4), 6-2.
Spanish great Rafael Nadal plays his quarter-final against Jordan Thompson later Friday.