The Dane - who was a runner-up at the tournament in 2008 - needed two hours and seven minutes to overcome the eighth seed 6-3 3-6 6-3 at the WTA International hard-court event on Friday.
Both players struggled on their own serve, with 11 breaks in total throughout the match.
But it was Wozniacki who found the crucial breakthrough in the sixth game of the decider, and sets up a final-four encounter with Sabine Lisicki.
The third seed also needed three sets to progress, as she ousted Italian Karin Knapp 7-5 4-6 6-0.
Lisicki is also a former runner-up at the event, having lost to Timea Bacsinszky in the 2009 final.
And her experience proved crucial as she curtailed Knapp's comeback by routing her opponent in the final set.
In the other half of the draw, Switzerland's Stefanie Vogele picked up a shock 6-3 3-6 6-2 victory over the United States' Sloane Stephens to set up a semi-final clash with Annika Beck.
Only two games went with the serve in a remarkable opening set, and things didn't improve for the remainder of the encounter, as just eight of the 17 remaining games finished in favour of the server.
But it was the Swiss who found her form in the final set, breaking her opponent on three occasions to book her place in the last four.
Germany's Beck had opened Friday's action with another tight contest - triumphing 6-3 6-7 (3-7) 7-6 (7-5) over qualifier Katarzyna Piter of Poland.
Following a relatively comfortable opening set, Beck found her opponent - ranked 87 places below her - in inspired form.
After finishing all square in the second, the Pole claimed a 7-3 tie-break victory, but was unable to build on her second-set win as she lost the decisive tie-break 7-5.