The former world No.1 was attempting to end a run of seven Sydney visits without getting past the quarter-finals at the Sydney International, but fell 7-5, 6-7 (7-6), 6-4.
Almost a third of the three-hour, 19-minute epic was played in over 40-degree heat.
Both players were treated for foot injuries during a gruelling second set on Ken Rosewall Arena, where they also battled mental demons at Homebush.
"It was brutal out there, and it was really hot. But you know, you just try and think like you're on a beach drinking pina coladas," Wozniacki said after the match.
"That's basically your train of thought. You know that it's the same for both players, so I was just trying to mentally just try and keep cool. But it was really, really hot out there."
"I thought we played actually some ready good tennis as well, considering all these conditions."
Wozniacki looked on track to end her barren run at Homebush when she battled back from 5-2 down in the second set, and then 5-0 in the tiebreaker, to force a third set.
The Dane broke the world No.19 twice in the decider, but gave up three games of her own and will now recuperate ahead of next week's Australian Open.
"On the positive side of things, I can eat whatever I want now because I have burned a lot of calories today. I'll definitely have an ice cream, for sure," she said.
Strycova is the first woman through to the semi-finals on day four and will now meet the winner of second-seed Agnieszka Radwanska and qualifier Ying-Ting Duan.
Bouchard wasn't on court for nearly as long but still felt the heat.
"It was really hot. It was pretty brutal," the Canadian said.
"All I was thinking about was the next changeover and drinking water and the ice towel, and wishing we had ice baths on the court ... (and trying) not to pass out.
"But luckily the match before us was so long that by the time we were out there, there were some clouds. By the end of the match, it was OK."
The Canadian star has now enjoyed three consecutive wins over top-30 opponents in Sydney as she aims to break a two-and-a-half-year title drought.
She will face Johanna Konta in the last four after the British No. 1 beat Daria Kasatkina 6-3, 7-5.
At a set and a break up, the sixth seed appeared to be coasting towards a last four place but her Russian opponent broke back immediately and then again to establish a 4-2 lead.
But Konta, who made 31 winners and 30 unforced errors, dug deep to win five of the next six games to seal victory in just under an hour and three-quarters.
The Press Association contributed to this report.