Pegula digs deep to stay alive in Adelaide
The second seed needed two-and-a-quarter hours to win the all-American battle 4-6, 6-2, 6-3 at Memorial Drive.
After splitting the first two sets, Pegula started the deciding set with a break, but lost it in the sixth game before breaking again for a 4-3 lead.
She dug deep to get through a seven-minute penultimate game, saving four break points for 5-3 then wrapping up the win.
"She was hitting well in the first set, there was not a lot more I could do," said Pegula.
"I stayed relaxed and tried not to get frustrated. I want to keep improving and have a good mindset.
"It's a brand new year and I want to find my confidence for the Australian Open."
Pegula has made the quarter-finals at the Australian Open in each of the past three tournaments.
She will next meet 2021 French Open finalist Pavlyuchenkova, who defeated Katerina Siniakova 2-6, 6-3, 6-2.
Laura Siegemund, part of Germany's United Cup winning team, advanced past Romanian Ana Bogdan 6-4, 7-5 with either Anna Kalinskaya or Daria Kasatkina awaiting her in the last eight.
In men's action, Chilean second seed Nicolas Jarry needed three-and-a-half hours to topple Italian Matteo Arnaldi 6-7 (5/7), 7-6 (9/7), 6-4, saving a match point in the second-set tiebreak.
Briton Jack Draper came through the day's second marathon, battling for 3hr 39min before finally advancing against Serb Miomir Kecmanovic 5-7, 7-6 (11/9), 7-6 (9/7).
In contrast, Australian Christopher O'Connell needed just 60 minutes to beat Russia's Alexander Shevchenko 6-3, 6-1.
At the WTA Hobart International, top seed Elise Mertens powered into the last eight with a 6-2, 6-3 thrashing of the Slovak Republic's Anna Karolina Schmiedlova.
She will face Arantxa Rus for a place in the semi-finals after the Spaniard swept past France's Varvara Gracheva 6-2, 6-3.
Chinese pair Zhu Lin and Yuan Yue also progressed.