Ostapenko beats heat to oust defending Brisbane champion Pliskova
The 26-year-old former French Open champion needed assistance from the trainer during the third set as she struggled with the heat and humidity.
But she managed to recover enough to overcome Pliskova in 2hr 13min.
"It was very, very humid and at one point I had really low energy," the third-seeded Ostapenko said.
"I'm coming from winter where it's minus 15 right now and here it's 35 degrees.
"It's a little bit different - it's the same for everyone but I need a little time to get used to it."
She will next face former world number one Azarenka, who survived a stern challenge from unheralded Frenchwoman Clara Burel.
Azarenka was on top early and raced to a 4-1 lead in the first set before Burel fought back and began to dominate.
But Azarenka rallied to win a close first set then ran away with the second to book a 7-5, 6-2 victory.
"I was trying to be aggressive and come to the net but I felt like she was really on top of me," two-time Australian Open champion Azarenka said.
"I felt I started really well, but maybe let her play her game a little bit too much, but it was a very competitive match.
"I was definitely much better in the second set in terms of accuracy and aggressiveness."
The Czech Republic's Linda Noskova also progressed to the quarter-finals with a 6-1, 6-7 (4/7), 6-3 win over Argentine qualifier Julia Riera.
In the men's draw, Australian wildcard Rinky Hijikata bounced back from losing the first set to see off Czech qualifier Tomas Machac 5-7, 6-2, 7-6 (7/4).
Fellow Australian Jordan Thompson also moved into the last eight when French opponent and fourth seed Ugo Humbert withdrew before the match due to illness.
Spanish great Rafael Nadal continues his comeback from a long injury absence against Australian Jason Kubler in an evening match on Pat Rafter Arena.