After coming out tight, the world number one began to swing more freely in the second and third sets, matching the Belarusian's power to emerge with a 3-6 6-1 6-4 victory and a spot in Saturday's final against Ons Jabeur (28).
"I needed to go all in to change the momentum," she told reporters.
"I felt a huge difference between the first set and the last two. I'm pretty happy that I got my level of energy up a little bit."
Sabalenka said she could feel the difference on her side of the net too.
"She was playing aggressively, and I was trying to stay in the game, which was my mistake," she said.
"I should just go for it."
Swiatek said learning to keep her composure even when her back is against the wall has been the most meaningful area of growth in her game.
"Earlier I felt like my emotions were taking over and I was panicking a little bit when I was losing," she said.
"Right now it's just easier for me to logically think what I can change. And I feel like I have more skills to do that and more than one type of way to play.
"I'm pretty happy that it changed because I think that's basically the most important thing on the highest level."
The two-time French Open champion said she is still learning to trust herself on the fast North American hard courts, where she struggled in tune-up events prior to coming to New York, after going on a 37-match winning streak earlier in the year.
"I trust myself for sure on clay, and maybe also other surfaces," she said.
"Here I just try to accept maybe that sometimes I'm not going to trust myself, and I still need to prove myself in a couple of matches against heavy hitters."
