After a one-sided start in a midnight match at Rod Laver Arena, Wozniacki met stiff resistance from the 39th-ranked Spaniard who dug deep to save a match point in the second set before outclassing the Dane in the tiebreak.
Second seed Wozniacki steadied herself, however, raising her game to bully Suarez Navarro from the baseline and grab another three match points on serve.
Wozniacki secured victory when Suarez Navarro hit long and she will meet Belgian Elise Mertens for a place in the final.
"I knew it wasn't going to be that easy ... In the second set I had the chance to close it out so I was disappointed I didn't do that," Wozniacki, who made the semi-finals in 2011, said on-court.
"I'm just proud that I managed to stay cool and finish it off in the third set," she added. "(Mertens) has had an amazing start to the year. It's going to be a tough one but I'm excited for it."
(Editing by Ed Osmond)
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