The Russian will next meet surprise semi-finalist Sybille Bammer of Austria, who crushed 13th seed Tatiana Golovin of France 6-2 6-3.
The 17-year-old Vaidisova troubled Kuznetsova in the first set with her powerful groundstrokes, big serves and aggressive returns.
"The match was high quality and to win it I had to put something into it," Kuznetsova told reporters. "I couldn't just defend. Usually I dictate and today she was doing that. She has extremely good strokes and serves well."
Kuznetsova gradually took control of the court with her heavy top-spin forehand but sixth seed Vaidisova did not lie down.
"She can be very unpredictable some moments, so I have to play every point," Kuznetsova said. "Sometimes she chooses extreme shots."
Former U.S. Open champion Kuznetsova has had a decent start to the year, reaching the Doha final, but she has yet to win a title.
"I'm doing better, improving my serve, coming more to net," she said. "I believe if I can keep doing this, I can improve as a player and my ranking will go higher."
The only mother ranked in the world's top 50, the 26-year-old Bammer reached her first Tier One semi-final thanks largely to her giant left-handed forehand and tricky serve.
Thee 46th-ranked Austrian completely knocked the French teenager out of her stride by mixing up her attack and taking care of every short ball that came her way.
"I tried to make her run because I thought when she can came into the court, it will be very difficult for me" Bammer said. "The players know me because I practise with them. Maybe they think that they have must beat me because they are better in the rankings than I am. Bu my game works better than before."
Bammer travels to tournaments with her five-year-old daughter Tina but she will reach the world's top 30 on Monday for the first time in her career.
"It's very good because I have my own family," she said. "My boyfriend and Tina, we are one family, and they stand behind me. It gives me a lot of power. And when I'm not on the court, I don't think 24 hours a day on tennis. I can also relax and do normal things."
Number 12 seed Li Na of China will face number 14 Daniela Hantuchova of Slovakia in the other semi-final.
