The camera caught Drake in what appeared to be wildly different moods as the match progressed - from mad, happy, concerned and even pensive.
Germany's Angelique Kerber, the highest women's seed remaining (11th), ousted Daria Kasatkina of Russian Federation in straight sets to advance to Thursday's other semifinal, in which she'll face Latvia's Jelena Ostapenko, who topped Dominika Cibulkova in straight sets.
Rare is the player who can produce Williams' sort of pace on serves - Giorgi's average speeds were actually faster on first and second serves, and she delivered the match's first three aces - and mirror her power in groundstroke exchanges at the baseline. There's a lot of things that I don't know if you can tell, but I really need to work on. "When I'm training, I have to be done at 1 p.m., because I've got to be with Olympia". "After the first set, I just said, 'Let's go three sets.' I just kept fighting".
"This is only my fourth tournament back so I don't feel pressure, I don't feel I have to win this". Serena? I don´t follow tennis, although I saw her in action.
But this nerveless comeback was a sight familiar to all who have admired Williams' warrior instincts throughout a Wimbledon career stretching back 20 years.
It was therefore a surprise to see Giorgi win the first set on Centre Court.
Williams is back in action at Wimbledon following a hiatus from the tennis circuit after becoming a mother a year ago.
Williams will feature in her 11th Wimbledon semi-final in the hunt for her eighth championship at SW19, and Julia Goerges will be her opponent on Thursday, having defeated Kiki Bertens 3-6, 7-5, 6-1.
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. "For me, there's so much further I want to go to get back where I was, and hopefully go beyond that".
Ostapenko hasn't dropped a set in her first five matches and the 12th seed said: "I'm just enjoying being here".
The professional tennis player is competing in the quarter finals of the competition, with Drizzy Drake cheering her on in the stands.
Goerges had failed to make it past the fourth round of any major before this tournament, and her best Wimbledon finishes were third-round appearances in 2010 and 2011.
Kerber takes on Latvia's Jelena Ostapenko in the other semi-final.