Muguruza, a qualifier into the draw who had already taken out No.5 seed Mona Barthel earlier in the week, fired nine aces and held nine of her 10 service games to beat Cibulkova in straights, 64 64.
The Spanish teenager's win over the World No.18 was her fourth Top 20 win, her first three all coming at either Indian Wells or Miami (No.9 Vera Zvonareva at 2012 Indian Wells, No.19 Ekaterina Makarova at 2013 Indian Wells and No.9 Caroline Wozniacki at 2013 Miami). This was her first one on grass.
And she'll have to do it again if she's to reach her first WTA final, as next up is the No.4 seed - and World No.20 - Kirsten Flipkens, who beat No.7 seed Urszula Radwanska by the same scoreline, 64 64.
Flipkens and Muguruza will be playing against each other for the first time.
There's a deeper rivalry about to resume in the other semifinal, with No.3 seed Carla Suárez Navarro taking on Simona Halep. Suárez Navarro was the first of the two to advance, fighting back from a set down and - after a lengthy rain delay - 2-0 down in the third to beat Tsvetana Pironkova, 26 64 64.
"Today was a very difficult match for me," Suárez Navarro said. "From the beginning I had to fight hard because she's a good player and she has been playing even better lately. The rain delay actually helped me relax, and I just tried to focus hard and I'm very happy I could finally win in the end."
Halep had a less complicated day, beating Ukrainian lucky loser Lesia Tsurenko in 69 minutes, 63 61.
"I was very nervous today - I don't know why," Halep said. "The weather wasn't so nice for us to play in, it was very humid, and the match was difficult, but I'm happy I'll play again in the semifinals."
Halep is now on an eight-match winning streak, having won her first WTA title in Nürnberg last week. There's only one negative with deep runs like this - missing things like the Pre-Wimbledon Party.
"I received the invitation - it's too bad I have to miss it this year," Halep commented. "But they have really nice player parties at every tournament, and I hope I can enjoy that one next time!"
Suárez Navarro leads Halep in their head-to-head series, 4-2, though they have never played on grass.
"I know Simona very well - we just played a few weeks ago, and she's always a tough opponent, fighting for every ball," Suárez Navarro said. "I'm happy to be here and I hope I play my best tennis."