Rizwan and Irfan both suffered hamstring injuries in the third match in Rawalpindi
The last-16 match pitted Vandeweghe's power against Wozniacki's consistency on Monday.
The American, ranked 25, was more aggressive and took more risks, and her strategy paid off - she fired 38 winners across the net compared with her opponent's 16.
She closed out the match with a break at the end of the second set, forcing an error from the 26-year-old Wozniacki with a ferocious cross-court forehand.
By reaching the quarter-finals, the 25-year-old Vandeweghe has matched her best performance at the All England Club. She will face Slovakia's Magdalena Rybarikova, ranked 87.