Williams was in danger of a stunning quarter-final exit after world number 52 Giorgi became the first player in this year's tournament to take a set off the former world number one.
She fought back to beat Italian Camila Giorgi 3-6 6-3 6-4 in a fiercely contested quarter-final on Tuesday.
And when Williams took the court for the second set, she did indeed look calm and composed - and roared back with a vengeance.
As Serena Williams prepares for her 35th Grand Slam semi-final, the American star says a fear of failure is driving her bid for an eighth Wimbledon title. Bertens won the first set 6-3 and was close to victory in the second before losing it 5 games to 7.
Williams is playing in her 11th semifinal at the tournament.
Serena Williams has warned her Wimbledon rivals that she is nowhere near her best despite powering into the quarter-finals without dropping a set.
"I feel good, I felt like I did better today, I had to, but this is only my fourth tournament back so I don't feel any pressure and have to win this", she said.
Serena Williams set a new record but played down title talk as she eased into the last-eight.
Williams had six aces and no double faults in the victory.
Giorgi had a bright start to the match, possibly catching Williams a little tired as she is still working her way back from the 14-month leave. "To be here, to be in the semi-finals", Williams said.
And it was the German 29-year-old who took control of the second set with a break.
"Neither of us remember my first steps, but the lessons I learned from the way she lives life are so appreciated", posted @KashifPasta.
The Dutch star finally tested Goerges' serve in the next game and she struck a superb victor on her way to securing the first break of the match.
"I have a long way to go".
"I don't really miss the tour but I miss the fighting competition".
Having crashed out in the first round at Wimbledon for five consecutive times, Goerges' emotions spilled over at the end of the match after she embraced Bertens at the net.
Kiki Bertens of the Netherlands loses a point to Julia Goerges of Germany during their women's quarterfinal match at the Wimbledon Tennis Championships in London, Tuesday July 10, 2018. However, the 13th seed has proved she knows how to win a close match. It's an honour to share the court with her.
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.
Will Kerber face Serena Williams or fellow German Julia Goerges in the final?
"It will be a different match that we played in Paris a few weeks ago", Del Potro said.
It took a period of accepting the nuances of the surface, to see the results that have taken her further than in any other Grand Slam.