The Dane dropped her three opening service games but broke back each time and went ahead 5-3, only to falter again and allow Petkovic to level at 5-5.
Once second seed Wozniacki clinched the opener with yet another break in the 12th game she began to dominate as her opponent lost patience in the baseline exchanges.
The second set was far more straightforward and the 2009 champion sealed her win with a drive volley into an open court after Petkovic had scooped up a drop shot.
"It was tough. She plays aggressive but I returned really well," Wozniacki said in a court-side interview.
She next faces Belinda Bencic after the Swiss player ended the run of British wildcard Johanna Konta 2-6 6-0 6-3 in the pre-Wimbledon event.
The other semi-final pits American Sloane Stephens, handed a walkover against injured Russian Daria Gavrilova, against former Wimbledon runner-up Agnieszka Radwanska who beat Bulgaria's Tsvetana Pironkova 6-2 6-2.
(Reporting by Martyn Herman, editing by Tony Jimenez)
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