The top seed, playing in her second match since a fourth-round defeat at the US Open that saw her drop to number two in the world rankings, sprayed the errors around in the opening set as Kudermetova grabbed a double break before going 4-0 up.
Swiatek finally got on board with a hold and looked to mount a comeback but could not prevent world number 19 Kudermetova from taking a set off her for the first time in five meetings.
Kudermetova surrendered the second set tamely, but she found herself ahead in the decider as Swiatek gifted her an early break with a double fault.
The Russian held her nerve towards the end of the contest and finished it off with a superb serve.
"I tried to just believe I can beat her. Today it happened. I'm really happy I managed to switch (the head-to-head) and win one match," said Kudermetova, who took full advantage of the 50 unforced errors from Swiatek's racket.
"In the last game, I just focused on playing the point. I don't need to hit aces. I think that was the key. I was ready to play the rally, not just finish with the serve."
Up next for Kudermetova is Anastasia Pavlyuchenkova, who reached her first semi-final since her run to the 2021 French Open final with a 6-2, 7-5 win over fellow Russian Ekaterina Alexandrova.
Pavlyuchenkova's career was derailed last year due to a knee injury that needed surgery, but she battled her way back to peak match fitness on the lower tours before reaching the Roland Garros quarter-finals in June.
"I think the most important (thing) is to be humble and play whatever you can to get back to the level," said Pavlyuchenkova.
"I was just working my way back to this level, trying to get back to the top. Just trying to enjoy, since I'm getting towards the end of my career."
Later, American second seed Jessica Pegula dropped her serve in the opening game of her encounter with Daria Kasatkina before producing a ruthless display to seal a 6-1 6-0 victory in 59 minutes and ease into her seventh semi-final of the season.
Pegula meets Guadalajara champion Maria Sakkari, after the fourth seed beat fifth seed Caroline Garcia 6-2 6-2.
"Being happy on the court really makes me play good. Smiling, enjoying," said Sakkari, who extended her winning streak to seven matches.
"There's a big process behind it. I just feel like the happier I am on the court and the more I smile on court, the better I play."