Spaniard Davidovich Fokina, world number 25, is aiming for a career-first ATP title in front of home support on Saturday.
"Today was a difficult match, I knew he was a very aggressive player," said Davidovich Fokina.
"I'm very happy with how I performed today."
In the other semi-final, American Quinn, ranked 63rd, eased to a comfortable 6-1, 6-2 victory over Portugal's Nuno Borges.