In front of a Centre Court crowd that included Justin Timberlake, Jessica Biel and Drake, Giorgi stood inside the baseline to return the Williams serve, never yielding ground and pushing the American to withstand her power.
Serena Williams is contesting her 35th major semifinal, and her 11th at Wimbledon. With the top 10 women having all been eliminated, No 11 Angela Kerber is the highest-seeded player left in the tournament. You could understand the 13th seed's bewilderment, after she came from a set down against Kiki Bertens to win 3-6, 7-6, 6-1.
Her next opponent will either be 13th seed Julia Görges, from German, or Croatian Donna Vekic. "After the first set, I just said, 'Let's go three sets.' I just kept fighting. I don't feel I have to win this; I don't feel I have to lose this", Williams said.
In a tournament that has been defined by all of the top seeds falling early and shrinking in tough moments, Williams showed exactly why she is always among the game's best, even if her ranking doesn't reflect it.
Kerber takes on Latvia's Jelena Ostapenko in the other semi-final. "It's 115, and she puts the ball close to the line".
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Cibulkova advanced to her third Wimbledon quarterfinal, following runs in 2011 and 2016.
Once Williams had figured out how to break the Giorgi serve, though, in the fourth game of the second set, the momentum changed.
Shot making and shot selection produced a clear gameplan for the fifth Italian woman to clinch the quarter-finals at Wimbledon, watched by the Fed Cup captain Tathiana Garbin, the first Italian player to beat a reigning world No.1 at WTA level (she defeated Justine Henin at 2004 French Open).
Incredibly, Goerges had won only five matches in 10 previous visits to The All England Club - and none in the past five years - before arriving last week.
"But I'm just very glad the way I handled everything today because it wasn't an easy match at all".
Williams is 3-0 against Goerges, winning in straight sets each time. She played a powerful game throughout - averaging a 112 miles per hour first serve on the day and had six total aces and 20 winners. "Everybody has the same chances to win that match, and I'm looking forward to it".