Goerges had to do it the hard way after coming from a set down against the Dutch No.20 seed to win 3-6 7-5 6-1 and set up a showdown with the formidable Serena Williams.
Williams took control of the third and final set in the the third game, claiming the third break of the match, and with the remaining games all going to serve, served out for a 3-6, 6-3 6-4 win.
Serena Williams is excited to face an opponent whose game she's familiar with in the Wimbledon quarterfinals.
"After the first set, I was like, 'All right, let's go three sets.' And that's kind of what I thought".
But that lifted a weight off her shoulders at the All England Club, where she has become the first Latvian to make a Wimbledon semi-final.
Ostapenko, the 12th seed, overpowered Slovak Dominika Cibulkova 7-5 6-4 to reach Wimbledon's final four for the first time, and without dropping a set.
Rare is the player who can produce Williams' sort of pace on serves - Giorgi's average speeds were actually faster on first and second serves, and she delivered the match's first three aces - and mirror her power in groundstroke exchanges at the baseline.
She said: "I think this match today was an example how much I've grown in this department, how much I've accepted". The 36-year-old rallied to win 3-6, 6-3, 6-4.
Serena Williams and her daughter Alexis Olympia watch the action during the first round of the 2018 Fed Cup at US Cellular Center on February 10, 2018 in Asheville, North Carolina.
Follow the LIVE updates from day 10 action of Wimbledon, where the spotlight would be on the two women's singles semifinals. "I'm happy to be in the second week, quarter-finals and now the semi-finals".
They traded breaks early in both sets before Ostapenko broke decisively for a 3-2 lead in the second when Cibulkova sent a forehand long. "I didn't expect to do this well in my fourth tournament back", Williams said. I'm just here just to be here and to prove that I'm back.
Kerber took advantage of Kasatkina's erratic serving and errors to return to the last four. She manages to hold on to her serve, but she can ill-afford such mistakes if wants to get back into the match.
With no top-10 seeds making the quarterfinals for the first time in Wimbledon history, 11th-seeded Kerber is the highest-ranked player left in the hunt for the Venus Rosewater Dish.
"I was down in the first set but I kept fighting".
Considering what she went through during a traumatic labour nine months ago, since when she has played only a handful of matches, Williams's physical condition has been impressive.
"You're only as good as your last win". The last time two German women reached any Grand Slam semifinals was at the 1993 French Open, featuring Steffi Graf and Anke Huber.
In contrast, Goerges is in the Wimbledon semi-finals for the first time.
"Every match starts from zero", Goerges said of her semifinal matchup against Williams.
Yet Goerges insists she can cause an massive upset against Williams.
It took a period of accepting the nuances of the surface, to see the results that have taken her further than in any other Grand Slam.