The world No.73 and ninth seed stormed past local wildcard Katherine Sebov in just 63 minutes, winning 6-1 6-0 in the final warm-up event before heading to Flushing Meadows.
The 28-year-old broke her opponent six times in nine service games to set up a quarter-final match with Xiyu Wang, after the Chinese world No.75 defeated another home player in Cadence Brace 7-6 (7-4) 6-1.
Saville is on the hunt for a second career WTA Tour title and was beaten at the semi-final stage of the Citi Open in Washington by Kaia Kanepi earlier this month.
The third, fourth and eighth seeds meanwhile were all eliminated on Wednesday. Italy's Jasmine Paolini lost 6-4 1-6 2-6 to Rebecca Marino while Anna Bondar and Tereza Martincova were knocked out in straight sets.
In Cleveland, Bernarda Pera extended her career-best winning streak to 12 matches, beating top-seeded Barbora Krejcikova of the Czech Republic 6-4 6-1 to reach the quarter-finals.
Pera, ranked world No.51, broke 2021 French Open champion Krejcikova four times in claiming eight of the final nine games. The 27-year-old has won her last two WTA 250 tournaments in Budapest and Hamburg.
Second seed Martina Trevisan of Italy withdrew with a left thigh injury, giving China's Zhang Shuai a walkover while third-seeded Ekaterina Alexandrova of Russia was upset by Madison Brengle 3-6 7-5 7-5 in their round-of-16 contest.
Alexandrova served for the match twice in the second set against No.63 Brengle, who fought off six match points in her 6-4 4-6 7-5 opening round victory over Varvara Gracheva at the US Open tune-up event.
The only remaining seeds are Aliaksandra Sasnovich of Belarus (seventh) and France's Alize Cornet (eighth). Sasnovich will take on Brengle, while Cornet will face Zhang in the quarters.