Even though seeded 25 coming into Wimbledon, the 23-time Grand Slam victor is ranked No.181 on the WTA tour and by beating Giorgi, she became the lowest ranked player to make the semifinal at Wimbledon.
Cibulkova is ranked 33rd in the world and controversially missed out on being seeded at Wimbledon when officials moved up seven-time champion Serena Williams into the seedings, despite the American being ranked outside the top 150 following her maternity leave.
Cibulkova faces Latvian 12th seed Jelena Ostapenko, a former French Open champion, for a place in the semi-finals.
In 2017, Ostapenko followed up her first Grand Slam title at the French Open by reaching the last eight at Wimbledon.
The 21-year-old 12th seed ended Dominika Cibulkova's inspired run with a 7-5 6-4 win before Kerber outclassed Russian 14th seed Daria Kasatkina 6-3 7-5. After losing the first set Aliaksandra Sasnovich failed to show the same level of game. "I'm just looking forward to my next match", Kerber said after making it through to her fourth quarter-finals at the All England Club. "Yes, I lost, but at the end I'm happy with my performance".
Kerber is now back in a grand slam title match for the first time since beating Karolina Pliskova in the 2016 US Open final - having started that year by stunning Serena Williams in the final of the Australian Open.
The 29-year-old put up a fierce stance on the court, responding very well on the returns before nailing down the winners; she had Ostapenko running around the court at times.
Cibulkova has won both of their previous matchups, but she isn't going to be focused on anything but what she has to do to reach her first Wimbledon semifinal: "I played her couple of times".
This semi-final was billed as attack versus defence and it was the solid, reliable manner of Kerber that prevailed as she let an erratic Ostapenko, who was going for winners on nearly every shot, hand her a swathe of free points.More news: Texas could gain ally in President Trump's Supreme Court nominee
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The German had a little too much nous for the unpredictable Kasatkina and will try to grab her first Wimbledon title.
"I feel like I am back, I still have a long way to where I was".
"I knew after the first set, "all right, let's go three sets".
Williams lifted her intensity and avoided facing any break points as she secured one break of her own to take the set 6-3.
An eighth Wimbledon title would also move her past Steffi Graf into second place on the list of female Wimbledon champions, behind nine-time victor Martina Navratilova.
In a match that featured eight breaks of serve - four in the first five games - Ostapenko was able to elevate her game in the crucial moments.
She defeated Dutch 20th seed Kiki Bertens 3-6, 7-5, 6-1 win on Tuesday. "We've played so many tough matches", Kerber said after she finally sealed the win on her seventh match point. "Sometimes. I'm also complaining because I think it was a wrong call".