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.
Williams will take on No.13 seed Julia Gorges of Germany, who also managed a comeback win against Kiki Bertens 3-6, 7-5, 6-1 to make her first appearance in the semifinals at the All England Club.
French Open champion Ostapenko, 21, was clearly the more adventurous player in her encounter with unseeded Cibulkova, pumping 33 winners and 28 unforced errors.
She'll play Jelena Ostapenko in the semi-finals on Thursday.
Ostapenko's shock first-round loss to Kateryna Kozlova at Roland Garros in May saw her drop out of the top-10. If there is one lesson I would teach my daughter it's never giving in, always fighting. Dominika played well but I fought until the end and was very confident.
The 29-year-old put up a fierce stance on the court, responding very well on the returns before nailing down the winners; she had Ostapenko running around the court at times.
Over the last week, Kerber has watched all the top 10 seeds perish, which has raised expectations that she could repeat her 2016 run here to the final.
"To be honest, I am not feeling the pressure because I am not looking who is left or not from the seeds".
Kerber, who offered up only a miserly seven free points, really just had to stay calm and wait for her opponent to self-destruct and Ostapenko fell into the trap.
Kerber will meet Jelena Ostapenko, the first Latvian woman to reach the semifinal at Wimbledon where she won the junior title in 2014. "I'm here just to be here and prove that I'm back", she said.
Giorgi won the sixth game and closed the gap a little, but Serena had upped her intensity level and took the set with a triumphant shout. But I'm going to prepare well for it, going to be probably long rallies.
"It's Love-40 and I was not winning my serve, so I was, like, Oh, my God, I need to go there and try to talk to the chair umpire and try to ask her to ask the referee to come".
Kasatkina was more competitive in the second set but Kerber broke to go 6-5 up, then served out the match.
It seems unusual that this will be the first time she has come up against Angelique Kerber on the tour - as the German defeated another youngster in Daria Kasatkina.
"For me I think everything is positive that I changed the coach".
The second set shaped the same way.
"She's playing with no fear".