It was Serena's 100th career main draw victory on grass.
Williams will play Julia Goerges, ranked No. 13.
I am fighting and it helps me gain more confidence with it.
"You never know what to expect from her [Ostapenko]", Cibulkova said.
"I don't feel pressure". I'm going to practise tomorrow, recover and get ready for the semi-finals'.
In a testament to her remarkable longevity, the former world number one has now made at least one Grand Slam final for the last 12 years.
Serena Williams is the undoubted comeback queen of tennis, but her Wimbledon semi-final opponent is enjoying quite the revival herself.
Incredibly, Goerges had won only five matches in 10 previous visits to The All England Club - and none in the past five years - before arriving last week.
The 21-year-old, who won the junior crown at Wimbledon four years ago, said: "Of course it's a big advantage that I have already a grand slam in my pocket because I had this opportunity to play those big matches already".
"I'm surprised she's playing so well".
Jelena Ostapenko hardly broke sweat as she beat Slovakia's Dominika Cibulkova and moved into the Wimbledon semi-finals for the first time.
After a insane and awesome final game Angelique Kerber, the only player to reach at least the quarter-final stage in each of the Grand Slams this season, reached the seventh major semifinal as she beat Daria Kasatkina for the fourth time in her career in seven meetings.
After more than a week of sizzling 30°C temperatures, the players struggled to find their range on a chilly and blustery Court One.
Jelena Ostapenko became the first Latvian woman to reach a Wimbledon semifinal with a 7-5, 6-4 victory over Dominika Cibulkova.
A relaxed, and arguably not even 100 per cent fit, Serena has proved just as unsafe, picking up where she left off two years ago when walking away with a seventh Wimbledon title.
"Angelique is a great player, it's going to be a battle, a tough match probably with long rallies, but I will prepare well and be confident".
Del Potro will face two-time champion Rafael Nadal in the quarterfinals on Wednesday.
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.
Del Potro looked flat as he was broken to trail 3-1 but he clawed his way back to lead 5-4 with his serve to come.
Kiki Bertens has paid tribute to her good friend and Wimbledon semi-finalist Julia Goerges, revealing a touching moment after their match on Court 1. She quickly surrendered her world No. 1 status after a fourth-round exit at the Australian Open and was upset in the first round at the French Open and US Open.
Cibulkova insisted after the match that the call should've remained in her favor.
The Latvian served the match at 5-4, coolly holding to love, firing a backhand victor on match point.