The 23-time Grand Slam champion dropped her first set of the championships but came through 3-6 6-3 6-4.

Giorgi, the world number 52, produced the type of power normally associated with her opponent - but the American then found an extra gear.

Williams faces German 13th seed Julia Gorges in Thursday's semi-finals.

Also through to the last four are German 11th seed Angelique Kerber, who beat Russian Daria Kasatkina 6-3 7-5, and Latvian 12th seed Jelena Ostapenko, who overcame Slovak Dominika Cibulkova 7-5 6-4.

Williams gets taste of own medicine

Before the match, Giorgi had raised eyebrows when, asked about her impression of Williams over the years, she said: "I don't follow women's tennis."

And she certainly played as if undaunted by the reputation and titles of her opponent.

Giorgi's serve was straight out of the Williams book of power. She delivered three aces to the American's one in the first set and won 84% of points on her first serve.

It is not often you see Williams scrambling to return a serve or nearly knocked off her feet by the force of a near 120mph delivery - it is more often her dishing that up - but she was given a taste of her own medicine by the fearless Giorgi.

The Italian's average serve speed in each set was higher than Williams', although the American recorded the fastest of the match at 122mph.

The 36-year-old came forward to attack more in the second set, not allowing Giorgi any break points and winning her own break in the fourth game, roaring "come on!" when winning key points.

She turned the screw with a backhand winner down the line to break in the third game of the final set and got more of her first serves in to take charge, sealing victory on her first match point when Giorgi sent a forehand into the net.

Can Williams win an eighth Wimbledon title?

Williams has recorded the second fastest serve of these championships at 122mph - just behind her sister Venus' serve of 123mph

Williams only returned to competitive singles tennis in March following the birth of her daughter but has nevertheless been the player to beat here.

With the top 10 seeds making early exits, she has yet to face a player ranked in the top 50. Against Giorgi, she answered any lingering doubts about what might happen if she faced a stiff test - showing she still has the stamina, spirit and shots to carry on collecting Grand Slam titles.

"I feel good, I feel like I did better today, I had to," she told BBC Sport.

"This is only my fourth tournament back so I don't feel pressure, I don't feel I have to win this. I still have a long way to go to be where I was."

The American could become the fourth mum to win a major, after Belgium's Kim Clijsters and Australians Evonne Goolagong Cawley and Margaret Court.

Victory would draw her level with Court's record of 24 Grand Slam crowns.

She will go into the record books as the lowest ranked player - at 181st - to reach a women's semi-final at Wimbledon; yet having dominated the game for so long, she is carrying on where she left off before her maternity break.

Camila Giorgi made a hasty exit from Centre Court after the defeat but has plenty of positives to think about

Analysis

Former world number one Andy Murray on BBC TV

It is something like her 35th Grand Slam semi-final, which is ridiculous. She looks in great shape.

After Indian Wells, she thought maybe she had come back a bit soon but she went away and did some intense training to get in shape for the French Open. It didn't quite work out for her then but she's looking great now.

It is tough to bet against her now she's got this far.