Konta, at a career-high world ranking of 18, hurt her hip and needed on-court treatment twice in the second set. She called the injury ''a small niggle'' and said she would play in Birmingham next week.
Saisai reached her first quarterfinals since February following losses in five consecutive main-draw opening matches.
She will face another local, 208th-ranked Tara Moore, who reached her maiden WTA quarters by upsetting eighth-seeded Christina McHale of the United States 6-2, 6-2.
Ashleigh Barty of Australia defeated Andrea Hlavackova of Slovakia 6-0, 4-6, 6-4 to set up a quarterfinal with top-seeded Karolina Pliskova of the Czech Republic.
Also, Tamira Paszek of Austria advanced when Magdalena Rybarikova of Slovakia retired with a right knee injury while trailing 6-3, 3-1.