Li represented a potentially tricky opponent despite her world ranking of 58, ranking second for aces with 22 from her first three matches.
The 25-year-old appeared confident as she chose to serve first after winning the coin toss, only for Pegula to break immediately.
Li improved after making 10 unforced errors and winning just 8% of her second serves during the first set, but Pegula seemed to raise her own game in response.
As always Pegula was strong on the baseline but made a conscious effort to move to the net as well. By contrast, Li tended to stay deep in a fruitless effort to keep up with Pegula’s powerful strokes.
“I felt really comfortable moving in today and coming in at the right times, it doesn’t always feel that good, but it started well and I wanted to keep executing that until the last game,” said Pegula.
“It’s a part of my game I can really use as a weapon. Sometimes I get stuck at the back because I’m so good there, but we’ve worked on that a lot and my coaches are happy when I’m finishing overheads and volleys at the net.”
In the quarter-finals Pegula will face either world number 62 Barbora Krejcikova or compatriot Taylor Townsend, the latter having eliminated former French Open champion Jelena Ostapenko and world number five Mirra Andreeva without dropping a set.
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