Winless in three previous meetings with Williams, including last month in Paris, Goerges could face compatriot Angelique Kerber in the first-ever all-German women's grand slam final if she somehow fashions a way to turn the tables.
Goerges is at the other end of the spectrum, preparing for her maiden major semi-final after also recovering from a set down to beat Dutchwoman Kiki Bertens 3-6 7-5 6-1.
Williams raised her intensity level, added some velocity to her groundstrokes and some decibels to her growls and powered back to win 3-6 6-3 6-4, a scoreline that was a touch closer than what actually transpired on court. "They will watch me play here at Wimbledon", she said.
She is now two wins from her eighth Wimbledon trophy and from tying Margaret Court for the most Grand Slam titles in history at 24.
Asked what she likes the most about the way Williams plays, Giorgi responded: "I don't follow tennis".
Serena Williams is not complaining about the high number of shocking results, but she could not resist a jab at the Wimbledon organizers, who only seeded her 25th despite her record.
Williams had six aces and no double faults in the victory. She must be aggressive, with the right degree of control, and has to test the stamina of Williams who has so far won a stack of short points and rarely been pushed around court.
The United States president Donald Trump is going to visit Great Britain this weekend and he will attend the men's singles semi-final at Wimbledon on Friday if John Isner reaches the semi-finals.
With two players that possess as much firepower, especially on serve as the Czech and the Dutchwoman, there didn't figure to be a lot of break chances, but it was Bertens who had the first opportunity. "I didn't expect to do this well in my fourth tournament back", Williams said.
"It was a very tough match but I was just trying to enjoy it".
In the third set, Camila held to register first on the scoreboard but Serena charged back immediately to hold her serve and then take Camila's serve at love to lead 3-1.
The 36-year-old Williams beat her next opponent, Julia Goerges, at the French Open with a fine serving display. "I still have a long way to go to be where I was". Sometimes I feel I can fight. A good start for her. When she served for it a second time, she needed to navigate a 16-point game that included five deuces and all of those match points, until forcing a forehand error on the last. The last time two German women reached any Grand Slam semifinals was at the 1993 French Open, featuring Steffi Graf and Anke Huber.
"This is tennis. Nobody is walking on the court saying OK, I'll give you a free match". She won 44 of the last 54 points she served.
Giorgi, Kasatkina, Bertens and Goerges will each be making her debut in the Wimbledon quarterfinals.