The pair battled for three hours and 20 minutes before the Czech claimed a 7-5 6-7 (6/8) 6-4 victory.
Strycova had seemed poised for victory in the second set but could not serve it out and then let a 5-0 lead in the tie-break slip away.
Konta through to last four in Sydney
There was a happy outcome in the end, though, for the world number 19, who next meets second seed Agnieszka Radwanska.
Wozniacki was able to look on the bright side, saying of the heat on wtatennis.com: " You just try and think like you're on a beach drinking pina coladas.
"I was just trying to mentally keep cool. But it was really, really hot out there. On the positive side of things, I can eat whatever I want now because I have burned a lot of calories today."
Radwanska was a much more comfortable 6-3 6-2 winner over qualifier Duan Ying-Ying, while the other semi-final will pit sixth seed Johanna Konta against Eugenie Bouchard.
Konta put an end to the run of Russian Daria Kasatkina, who defeated world number one Angelique Kerber in round two, winning 6-3 7-5.
Bouchard, meanwhile, continued her encouraging form with a 6-2 6-3 victory over Anastasia Pavlyuchenkova.
The Canadian won her only previous clash with Konta in the second round of Wimbledon last year.
At the Hobart International, top seed Kiki Bertens reached the quarter-finals with a 6-1 6-4 win over Galina Voskoboeva.
Japanese qualifier Risa Ozaki knocked out former top-five player Lucie Safarova while there were also wins for Lesia Tsurenko and Shelby Rogers.
Konta through to Sydney quarter-finals
Kerber suffers shock defeat in Sydney