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.
When Williams was asked her expectations after winning her first match at Wimbledon in two years, she said, "Not only do I expect to win, I expect to win emphatically".
Goerges turned out to be an unstoppable force as she won eight of the last nine games to subdue her friend, whose lunging effort on match point rolled into the bottom of the net.
Though she was able to halt Williams' momentum and a run of four successive games, Giorgi could not prevent her from forcing a third set, the 36-year-old letting out a huge roar as she clinched the second.
She gave birth to daughter Olympia in September.
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"I said to her, "You don't have to be sorry", Bertens said. But also I've never been ranked where I am when this has happened before, so usually I'm one of those few seeds left that's still fighting and still in the tournament.
The key game was when Williams powered to a 2-1 lead in the decisive set, against the serve, without conceding a point. "This is only my fourth tournament back", she said.
"For me, there's so much farther I want to go to get back where I was, and hopefully go beyond that".
Many seeded players lost in the men's and women's singles events in the Wimbledon first week. Kerber (No. 11) is the highest remaining seed, followed by the No. 12 Ostapenko, No. 13 Goerges, No. 14 Kasatkina, No. 20 Bertens and No. 25 Williams.
"At the French Open I had all that pressure, now it's gone", former junior Wimbledon champion Ostapenko said.
It was a fearless performance that offered Williams one of her toughest tests since returning. For whatever reason, today I was so calm.