Williams was in danger of a stunning quarter-final exit after world number 52 Giorgi became the first player in this year's tournament to take a set off the former world number one.
Kerber has a chance to set up a rematch with Williams after losing the 2016 final to the American - although if she and Goerges win, it would be the first all-German women's final since 1931.
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".
The 2011 French Open and 2014 Australian Open champion is not tempted to make a comeback of her own, as she watches seven-time Wimbledon victor Williams compete at the All England Club for the first time since the U.S. great won the 2016 title.
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.
This is just her fourth tournament back since giving birth last September, and Williams is one win away from a 10th Wimbledon singles final appearance.
But the 29-year-old has erased those painful memories with a superb run, capped by a come from behind success against Bertens in her first Grand Slam quarter-final. "I'm OK, I feel good, I feel like I did better today, I had to".
But the third set was all Williams, and she recorded six of her seven aces - making it clear she's moved well past the pectoral injury that forced her to withdraw ahead of the fourth round in Paris - and seemed to be in control throughout.
Williams revealed she does not want her daughter to follow in her footsteps.
Goerges and Kerber have already accomplished something not seen at Wimbledon since 1931 by putting two Germans in the women's semifinals.
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Republicans have said they disagree with that conclusion, which will likely be a significant focus of Thursday's public hearing. If the full House does vote to hold someone in contempt, the matter then moves to the courts, where it has often stalled.
Williams has fallen 13 times in Grand Slam quarter-finals - more than in any other round - but was never panicked.
"I said, 'All right, ' " said Williams, who hadn't dropped a set the entire tournament before Tuesday. "To me, it's scary how close she is to being back to her best level".
Surprisingly, the Czech faced another break point in the fifth game, but this time, some deep hitting off of the forehand wing produced an error from Bertens and she dug out a hold to remain just one break down.
The Queen is back, with Tuesday's win guaranteeing that she will jump from 181 to at least 51 when the new rankings are announced next week.
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.
Having crashed out in the first round at Wimbledon for five consecutive times, Goerges' emotions spilled over at the end of the match after she embraced Bertens at the net.
"I have a long way to go".
"You feel you get a little bit tight, especially if you have your third or fourth match point again. She (Ostapenko) won a Grand Slam, as well".
"Every match starts from zero", Goerges said of her semifinal matchup against Williams. It's an honour to share the court with her.