Williams took the set in convincing fashion, 6-3, and yelled her trademark, "Come on!" as she clinched the final point.
Serena, who is targeting an eighth title at SW19, is eyeing a first Grand Slam after taking a break from the sport for the birth of her first child. Despite the two-year gap since their previous meeting, Williams professed to having watched 52nd-ranked Giorgi play "a lot".
If she gets past that challenge, a match-up with either Kiki Bertens or Julia Goerges will await in the last four.
"Every match starts from zero", Goerges said of her semifinal matchup against Williams.
Cibulkova did her best to try and hang on but the Slovakian was left chasing shadows as Ostapenko blasted a backhand victor on her first match point to reach the last four without dropping a set in this year's tournament.
The Canadian rapper, 31, couldn't help but smile as he showed up to another of the icon's grand slam tennis matches, with the star vying for her 24th single Grand Slam title, and her first since welcoming baby daughter Alexis in September.
"Sometimes I feel, 'Man, I'm in trouble, ' she said after the match".
It's okay, Serena, just keep your eyes on the prize at Wimbledon! "But I feel like I'm back".
It took Mannarino so much toil and trouble to win one game, saving four break points to hold to begin the second set.
Still, Williams said she's not getting too excited as she's still adjusting to tennis after returning from maternity leave.
"It sounds insane to maybe have the chance to share a German final in Wimbledon".
In June, she was a match away from the French Open quarterfinals before withdrawing from the tournament an hour before her anticipated match against Maria Sharapova.
Two-time grand slam victor Angelique Kerber faces 2017 French Open victor Jelena Ostapenko in the other semifinal after the pair downed Daria Kasatkina 6-3 7-5 and Dominika Cibulkova 7-5 6-4, respectively.
"I'm ok, I feel good, I feel like I did better today, I had to".
The Queen is back, with Tuesday's win guaranteeing that she will jump from 181 to at least 51 when the new rankings are announced next week.
Ostapenko reached the last eight for the second straight year with a 7-6 (4), 6-0 victory over Aliaksandra Sasnovich, while Cibulkova beat Hsieh Su-Wei 6-4, 6-1.