Sasnovich surrendered the two hour 16 minute tussle with her 56th unforced error of the match.
Wozniacki seemed irritated by the tension of the strings on her racket and discarded it midway through the second game of the match. That failed to improve her focus as she continued to tug the strings between points throughout the contest.
Sasnovich raced out to a 4-1 lead in the first with the help of some deft dropshots and it seemed that the world number 49 was well on her way to pulling off a major upset.
But she was undone by 14 double faults.
Wozniacki reeled off five straight games to take the first set and, despite dropping the second set amid service issues of her own, was able to advance.
Next up for the 27-year-old Dane, who needs to win the tournament and hope that top seed Simona Halep fails to reach the final, is either out-of-form U.S. Open champion Sloane Stephens or Russian Daria Kasatkina.
Halep narrowly avoided falling to world number 165 Caroline Dolehide on Sunday and faces unseeded Chinese Wang Qiang on Tuesday.
(Reporting by Rory Carroll, editing by Pritha Sarkar)
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