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The Dane had dominated the match until she was 5-4 and 30-0 up as she served for the victory but suffered a bout of nerves which her 22-year-old opponent fully exploited to draw level.
Wozniacki recovered her composure, though, and saved two set points before dominating the tiebreak to seal a title-decider on Saturday against either Simona Halep or Angelique Kerber.
Wozniacki, who has yet to win a grand slam title despite spending 67 weeks as world number one, sealed the victory and a place in her third major final when Mertens dumped a backhand into the net after 97 minutes.