Pegula is the highest seed left in the women's draw after Iga Swiatek (21) and Ons Jabeur (28) were knocked out in first-week upsets.
Although Pegula says she feels "weird being a favourite", she also feels confident and more settled than she has been in the past.
"I have a great shot here. Throughout the whole tournament I've been playing the best I have than in any of my other Grand Slam quarter-finals. That I think helps," Pegula said.
"I think I feel more experience coming in here... I would say I definitely feel very confident going into this quarter-final, that I'm playing the best tennis and I have a very good chance of making a semi."
Azarenka is back in the quarter-finals in Melbourne for the first time since she became a mother and is out for revenge after she was knocked out by Pegula in 2021.
"She's an amazing player... She got me here, so I definitely want revenge," said the Belarusian, who won the title in 2012 and 2013.
Wimbledon champion Elena Rybakina (23) of Kazakhstan toppled world number one Swiatek and faces another former Grand Slam champion in Jelena Ostapenko (25) of Latvia.
Ostapenko won the French Open in 2017 two days after turning 20, but she has only reached one more Grand Slam semi-final since as she struggled to replicate that form and consistency while she came to terms with the sudden fame.
"My life changed a lot (after winning the French Open), so I needed a few years to really get used to what happened because I was really young," Ostapenko said after knocking out another American favourite Coco Gauff (18).
"You became more popular in your country. Everybody is watching you. Of course, it's great, but I needed some time to get used to it.
"Sometimes I can go a little bit too much, but I'm an emotional person in general. So it's always hard to find this balance."
