Dutchwoman Kiki Bertens takes on German 13th seed Julia Goerges in the final quarter-final.
Cibulkova did her best to hang on but was left chasing shadows as Ostapenko blasted a backhand victor on her first match point to become the only woman to reach the semis without dropping a set in this year's tournament.
In the third Wimbledon quarterfinal of her career, Cibulkova will face 2017 French Open champion Jelena Ostapenko, who also overcame a disagreement with an official on her way to reaching the last eight.
With Ostapenko and her compatriot Ernests Gulbis both making the second week at Wimbledon this fortnight, it's the first time in history that multiple Latvian players have made it this far at the same Grand Slam.
The Latvian 2017 French Open champion, lost in the first round of her title defence in Paris six weeks ago, but is back on a mission on the lawns of south-west London and booked herself a spot in the quarter-finals with a 7-6 (4), 6-0 over Aliaksandra Sasnovich on Monday.
Kerber is seeded 11th and, after a week of shock defeats for her title rivals, that makes her the highest ranked woman left in the draw. Giorgi gave Williams a battle, with Williams dropping the first set. "I'm fighting until the end and I'm gaining more confidence".
"It really messed with me, then I tried to just calm down, to play my game".
Now she played in the quarters of Wimbledon for the first time against the experienced former No1 Kerber, who was runner-up here in 2016-the year she won both her Majors. "We are here in the semis and they are all tough opponents and you have to play at your best", Kerber said after clubbing 33 winners to Kasatkina's 16.
She quickly worked out a way to hurt the 23-time grand slam champion and it was not just her clothes that were eye-catching as some impressive serving and a barrage of cross-court forehands saw her dominate.
"I never thought I was in danger of losing this match". It's great to be in the semis.
"I was running everywhere on the court, she was moving me very much!"
Perhaps she needs to stop thinking about Serena's status.
"I still have a long way to go to be where I was". "I'm just pleased with my game today". Up 5-4, Williams got to serve for the match, and she won the game easily.
No 11 seed Kerber defeated Daria Kasatkina 6-3 7-5 on Centre Court in Tuesday's last-eight tie. She looks in great shape.
"Sometimes I'm also complaining because I think it was a wrong call".
But the crucial game in the first set went Ostapenko's way as she broke to love for a 6-5 lead and served it out with two aces to complete a run of nine straight points her way.
Asked whether she had sympathy for Hsieh, Cibulkova was adamant it was not the Taiwanese player who had been wronged.