Having beaten Swede Mirjam Bjorklund in three sets to open her campaign, a resurgent Saville saw off American Pegula 7-5 6-4 in 98 minutes for her second top-10 win of the season.
The Australian will face Rebecca Marino in the last eight after the 31-year-old Canadian defeated Germany's Andrea Petkovic 6-3 3-6 6-1.
In the first meeting between the two, it started to go wrong for Pegula in the ninth game of the opening set as Saville broke to love.
Pegula, who won her first WTA singles title at the most recent edition of the Citi Open in 2019, immediately broke back before dropped her serve again. Saville closed it out at her second opportunity.
The Aussie broke serve in the first game of the second set and after Pegula had six chances to break back over the remainder of the match, Saville saved every one to close out the win.
Saville is now into her third quarter-final of the year, all on hard courts, after Miami and Guadalajara.
She was ranked as low as world No.627 as recently as February this year, following Achilles tendon surgery which kept her out of action for almost the entire 2021 season.
But the 28-year-old has charged back into the Top 100, also bolstered by a round-of-16 showing at Indian Wells where she beat world No.5 and Wimbledon finalist Ons Jabeur.
