Barty battles past Pliskova to reach Stuttgart semi-finals
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"It was an incredible match, with two very different opening sets, and the third was extraordinary," said Barty after her 18th win this year.
"I felt like I created a lot of opportunities and Karolina was able to come up with some quality stuff on some massive points.
"It was a really good battle."
However, Barty broke the Czech to start the second set and begin her recovery.
Barty then held to love and secured victory in the following game on her second match point.
"I missed some returns, but Karolina is a fierce competitor who has been at the top of her game for a long time," said Barty.
"I knew I'd have to do something special to claw my way back and get back on my terms."
The 2019 French Open winner will face either Petra Kvitova, the 2019 Stuttgart champion, or fourth seed Elina Svitolina in Saturday's semi-final.