For the first time in the tournament, the 36-year-old was seriously challenged as unseeded Giorgi, playing in her first Grand Slam quarter-final, fought fire with fire to claim the opening set on Centre Court.
Williams, a seven-time Wimbledon champion, was in danger of a stunning exit after world No 52 Giorgi became the first player in this year's tournament to take a set off the former world No 1.
Kerber came out on top in a spectacular 25-shot rally to force match point number seven and finally got the job done as Kasatkina netted a forehand, the German a relieved 6-3 7-5 victor.
Williams, who won the Wimbledon title on her last two visits in 2015 and 2016, is now on an 18-match winning streak at the All England Club.
"I faced a thousand and three seeds in my life, so I'm okay", she said. "But I notice she plays that way against everybody". "For me, there's so much farther I want to go to get back where I was - and hopefully go beyond that".
The 90th Wimbledon win of her career - the most among active female players - means Serena, now 181st in the WTA rankings, will return to the top 100 next week.
"I mean, I always say I plan on it, I would like to be there, have these goals".
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Ostapenko struggled with the pressure of defending her maiden Grand Slam title, losing in the first round of the recent French Open. This semifinal is the 11th of her decorated career at the All England Club. It's like all the other women that are still in the draw.
Pliskova's exit means that for the first time in the Open era, no top ten seeds on the Ladies' side reached the quarterfinals at the All-England Club as Bertens sets up a last eight tie with 13th seed Julia Goerges with the victor advancing to their first Wimbledon semifinal.
In February, in her first competitive match in more than a year, she moved slowly while playing a Fed Cup doubles match with her sister, Venus.
Ostapenko was more efficient, serving her match out at love and converting her first match point with her 14th backhand victor.
Williams kept her opponent at bay, sending Giorgi scampering back and forth across the baseline with a range of shots proving she's back to very near her best.
Angelique Kerber is now the highest-ranked player left in the tournament.
The fifth-seeded del Potro failed to convert four match points when serving at 5-4 in the fourth set, but maintained his composure to close out the contest with his first opportunity in the tiebreaker that followed. Tennis player from Latvia habitually acted in the most aggressive manner for two sets, which was made five breaks and five times surpassed the competitor by actively won balls.