Twenty years after making her Wimbledon debut, Williams looks as good as ever and she moves into the quarter-finals without dropping a set in her first four matches.
Williams' seemingly inevitable march to the final of a women's singles tournament in which none of the top 10 seeds remain continued against Evgeniya Rodina as she eased into the quarterfinals, but the seven-time Wimbledon champion needed to use much more of her reserves against Giorgi.
Williams was forced to withdraw from the fourth round of the French Open last month in her grand slam return with a pectoral injury and admitted last week she still wasn't serving at full power.
The 36-year-old will play German 13th seed Julia Goerges on Thursday for a place in Saturday's final boasting a 3-0 career record.
Germany's Goerges came from a set down on Court No 1 to defeat her friend and occasional doubles partner Kiki Bertens, the Dutch No 20 seed.
Thursday's (Friday NZT) other semifinal will also feature a German, two-time grand slam champion Angelique Kerber, against 2017 French Open victor Jelena Ostapenko of Latvia.
The 12th-seeded Ostapenko is the second-highest-ranked player left in the draw and faces Dominika Cibulkova next after the Slovakian world number 33 continued her defiant run with a 6-4 6-1 victory over Su-Wei Hseih.
After a series of upsets made this edition of Wimbledon the first since it began seeding players in the 1920s that none of the top 10 women reached the quarterfinals, Nos.
"I was down in the first set but I kept fighting". 'I'm getting there. Yeah, I don't think I'm there yet.
"I just tried to fight for every point", the 29-year-old said after finally reaching the last four of a major on her 42nd attempt.
Goerges had gone out in the first round at Wimbledon for the past five years. "Just the fewer the better for me!"
Kerber, the 2016 Australian and US Open champion, said: "I mean, the pressure is not always on my side".