Belarusian 24th seed outlasted her American opponent in a marathon match setting up a last-four encounter against Wimbledon champion Elena Rybakina at Melbourne Park.
Peng Shuai alleged on social media in November that former Chinese vice-premier Zhang Gaoli forced her into sex during a long-term on-off relationship.
Japan's Naomi Osaka, the fourth seed, has overcome her unseeded opponent 1-6, 6-3, 6-3 inside a near-empty Arthur Ashe Stadium at Flushing Meadows.
Venus Williams upended defending champion Johanna Konta 5-7 6-1 6-2 on Monday to reach the Miami Open quarter-finals while a dominant Victoria Azarenka also advanced with a straightforward win over Agnieszka Radwanska.
More than seven years after appearing in her first Grand Slam final at the 2009 US Open, Wozniacki can finally erase the "but never won a major" footnote that has long been attached to her resume.
Other doubtful starters for the grass court Grand Slam include Victoria Azarenka and Jo-Wilfried Tsonga.
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