The No.2-seeded Vinci was the favorite for the title after No.1 seed Angelique Kerber's withdrawal, but it wasn't to be as the No.8-seeded Kuznetsova scored a 62 63 win over her in an hour and 18 minutes.
"I took revenge - I lost to her the last time we played in Dubai," Kuznetsova said. "It can be very uncomfortable to play against her game, but I was just patient, and that was the most important thing."
Kuznetsova is now through to the semifinals here for the second time - she also made it this far back in 2007 before falling to Serena Williams (who in turn was beaten in the final by Elena Dementieva).
"It's great to play back at home," Kuznetsova said. "I'm really enjoying the time here, I feel like I'm playing much better this part of the season, and I think all of my hard work has worked out for me."
Next up for Kuznetsova is No.7 seed Samantha Stosur, who won 10 of 13 games from 3-0 down in the first set to completely take control against Ivanovic, eventually finishing off the No.4 seed, 75 64.
"I certainly had a few things in my head today that I wanted to try against her," Stosur said. "Right from the start it was all kind of working and my confidence started to build, and I was able to play well right through to the end of the match. So I'm pretty happy with how everything went out there today."
Stosur is through to the semifinals here for the second time as well - she made it all the way to the final here last year, falling to Caroline Wozniacki in three dramatic sets (read more about that here).
"I've managed to play well here the last few years for sure," Stosur said. "Sometimes the court here feels a little bit strange, but I think the way that I play I can really hit through the ball and use my power, and things have been working well for me. So I definitely enjoy playing on this surface here."
Stosur and Kuznetsova are tied in their head-to-head series, 3-3. The rivalry has swung in Stosur's favor as of late though - the Australian has won both of their previous 2013 meetings in straight sets.
The other semifinal will pit Simona Halep against Anastasia Pavlyuchenkova. The No.5-seeded Halep was the first to win, beating Russian wildcard Alisa Kleybanova, 61 61; Pavlyuchenkova followed her into the semis at night, winning the first seven games and closing Daniela Hantuchova out, 60 64.
"I'm happy to be in the semifinals," Halep said. "It was a great match for me today. Alisa hits the ball very strong, but I moved better and was hitting the ball well too. I felt really good on the court."
"After seven years of losing first round here all the time, I'm extremely happy and pleased with my performance so far," Pavlyuchenkova said. "I've started feeling better and better with every tournament at the end of the year. I've been working on my weaknesses with my dad and I'm happy it's working."
Halep has beaten Pavlyuchenkova in both previous meetings, including a few weeks ago in Tokyo.