But Serena bludgeoned her way out of trouble over the final two sets to stay on course for an eighth All England Club triumph.
It was Serena's 100th career main draw victory on grass.
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.
"I knew after the first set, 'all right, let's go three sets'. I'll just keep fighting," Williams said.
"I'm ok, I feel good, I feel like I did better today, I had to.
"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."
Serena is the first woman to reach a Grand Slam semi-final without facing a top 40 ranked opponent since 2013 and just the fourth since 2005.
Her path to the title has been wide open from early in the tournament as Garbine Muguruza, Maria Sharapova, Simona Halep, Petra Kvitova, Venus Williams, Caroline Wozniacki and Sloane Stephens have all been eliminated.
Kerber takes on Latvia's Jelena Ostapenko in the other semi-final.
- Select group -
If Serena lifts the Venus Rosewater Dish this weekend, she will join an select group of women who have won Grand Slam titles after becoming mothers.
She would also draw level with record holder Margaret Court on 24 Grand Slam crowns.
Williams won Wimbledon on her last two visits in 2015 and 2016 before missing last year's event due to her pregnancy.
Watched from the stands by her friend and mega-star rapper Drake, Serena struggled to hit the right notes in the first set.
There were no signs of stage-fright from Giorgi in her first Grand Slam quarter-final as she took the first set.
But, hitting her serve with more ferocity, Serena wrestled back control of the match with a crucial break in the fourth game of the second set.
Shrieking and clenching her fists after every key point that went her way, Serena let out a gutteral 'C'mon' once she wrapped up the set.
It was a verbal and physical assault that Giorgi couldn't withstand.
Asked before the match what she made of Serena's form, Giorgi had replied: "I don't know, I don't follow women's tennis." But this nerveless comeback was a sight familiar to all who have admired Williams' warrior instincts throughout a Wimbledon career stretching back 20 years.
When Serena broke again for a 2-1 lead in the final set, the American whirled and pumped her arms.
Her dance of delight signalled the end of Giorgi's threat as Williams raced to the finish line.
(This story has not been edited by Business Standard staff and is auto-generated from a syndicated feed.)