With this victory, Kerber is guaranteed to remain in the Top 10. "After the first set, I just said, 'Let's go three sets.' I just kept fighting". I just tried to fight for every point.
Giorgi, when asked going into the match against Williams whether she would watch her opponent on tape, responded, "I don't follow tennis, women's tennis". "I have a long way to go".
She was the only quarter-finalist from previous year to reach the last eight and is now through to her second grand slam semi-final having not dropped a set.
All eyes were on 36-year-old mum Williams to see how she would respond to such a challenge to her supremacy at Wimbledon, where she is unbeaten since 2014.
Having shaken off the rust following her lengthy lay-off after the birth of her daughter Olympia in September, Williams is on the verge of a 10th Wimbledon final appearance. Up 5-4, Williams got to serve for the match, and she won the game easily.
But with none of the top eight seeds left in the draw, she is now a huge favourite to claim a 24th Grand Slam title and move level with Margaret Court on the all-time list.
Kerber, who won the Australian and US Open titles in 2016, will be playing in the seventh Grand Slam semifinal of her career. "Just stay tuned, right?"
"I think it's everything worth it for the season I'm playing now, that I'm sitting here right now, I'm able to play on Thursday semi-final against Serena Williams".
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She lost only four points on it in the opening set, all of them in the sixth game when a courageous Giorgi rifled a backhand deep into enemy territory to snatch a break out of nowhere, setting the Centre Court crowd abuzz.
But she was broken in the first set as Giorgi took 16 of 19 points behind her first serve and even saved four break points as she tried to consolidate.
The fifth seed had led by two sets Monday but Simon grabbed the third set before fading light ended play.
Del Potro will face two-time champion Rafael Nadal in the quarterfinals on Wednesday.
The Slovak player downing Hsieh Su-Wei in straight sets, 6-4 6-1, to reach the quarter-finals for a third time.
Williams, who had rapper Drake as part of her entourage, had to survive a 0-30 service game early in the second set and that was a defining moment in the match as she soon took command by breaking Giorgi, which proved enough to decide the second set.
"This is tennis. Nobody is walking on the court saying OK, I'll give you a free match".
Kasatkina saved two break points at 4-1, the second with an emphatic airborne backhand victor, and forced two of her own in the next, winning a ferocious rally with a flashing forehand to bring them back on serve.