Top seed Muguruza, playing in the first match of the day, eased through her quarter-final 6-1 6-3 against the fifth seed at Stanford University in California, breaking the 19-year-old Croat five times in a match that lasted barely an hour.
"I think today I was very accurate," said the Spaniard in an on-court interview. "Ana is such a powerful player and super young, I knew I had to be concentrated.
Keys stuns Wimbledon champion Muguruza
"I had to match her, be aggressive as well. I'm happy that I did it, and that it didn't turn bad in the second set.
"I think she served a little bit better, and did less mistakes ... made the match a little bit more equal. It was a little tougher in the second set."]
Local product Bellis is one of three Americans in the semi-finals along with Coco Vandeweghe and Madison Keys.
Kvitova dropped the first game to love on serve and it did not get much better from there as she ran up 26 unforced errors.
The Czech missed six months after being stabbed in her left hand by an intruder at her home in the Czech Republic in December.
Bellis, ranked 44th in the world, will take on fellow Californian Vandeweghe in a Saturday semi-final, while Muguruza will face third-seed Keys.
Results from the Stanford Classic Women's Singles Quarterfinal matches on Friday
- 8-Catherine Bellis (U.S.) beat 2-Petra Kvitova (Czech Republic) 6-2 6-0
- 3-Madison Keys (U.S.) beat 7-Lesia Tsurenko (Ukraine) 6-4 6-3
- 6-CoCo Vandeweghe (U.S.) beat 4-Anastasia Pavlyuchenkova (Russia) 6-2 6-3
- 1-Garbine Muguruza Blanco (Spain) beat 5-Ana Konjuh (Croatia) 6-1 6-3
Sharapova withdraws from Stanford Classic with injury
Norrie to ask Murray and Evans for advice ahead of Berrettini final clash