For the first half of the match it looked as though experience would prevail, as Errani's backboard-like game built her a 64 22 lead - but Bencic took complete control of the match from there, reeling off nine straight games to win the second set and go up 5-0 in the third. She would close it out, 46 62 61.
"She played really well. I had problems in the beginning because it was our first time playing and I didn't know her game so well," Bencic said. "But then I adapted and stepped in for the spin balls.
"I just kept trying to focus on the next points and not the score, and I managed to play more and more aggressively and step in more. That was the key. I started serving better after the first set too."
Not only is the 17-year-old Bencic now through to her first WTA semifinal, but before this tournament she had never even won back-to-back main draw matches at the WTA level. And she almost didn't even make the main draw here - she faced a point for a 4-1 third set deficit in her last qualies match.
The Swiss' win over the No.11-ranked Errani was also the first Top 20 victory of her career.
"For sure it's my biggest win. I can't believe it. I can't believe I'm playing the semifinals here from qualies," she said. "I didn't see these results coming, but I was hoping for them, and I was believing that someday they will come. I'm just really happy they came this week here in Charleston."
"I was following those players and I was also following this tournament, and I knew they had great success here," Bencic said. "And I'm very happy that I can now have great success here also."
Next up for Bencic is another surprise package - Jana Cepelova, who had already taken out No.1 seed Serena Williams and No.13 seed Elena Vesnina earlier in the tournament, dropped a 62 61 decision on No.12 seed and fellow Slovak Daniela Hantuchova in the feature night match on center court.
Like Bencic, Cepelova is now through to the first WTA semifinal of her young career.
"I'm really happy," she said. "It was a tough match. Daniela is a good player, and she's my good friend, so every time you play each other it's very tough. But I'm really happy I won here tonight.
"It's my first semifinal, and I'm happy it's in a nice city like Charleston."
Cepelova and Bencic will be playing against each other for the first time.