The seven-time champion, who missed the tournament previous year, was outplayed by Italian Camila Giorgi initially but fought back impressively to win 3-6 6-3 6-4 on Centre Court.
She got to deuce in the next Pliskova service game, but neither player would have another break chance and the set went to a tiebreak, Bertens sprinting out to a 5-0 lead.
The Latvian struck 32 winners to just six from her opponent, with Cibulkova's second serve taking a pummelling, and won 7-5 6-4 in an hour and 22 minutes.
Williams is playing in her 11th semifinal at the tournament.
She would also draw level with record holder Margaret Court on 24 Grand Slam crowns.
The 26-year-old, who was contemplating retirement last year after losing her enthusiasm for the sport, was the first Dutch woman to reach the Wimbledon quarter-finals since Michaella Krajicek in 2007.
Seventeen months ago, Williams won her last major, the 2017 Australian Open, while pregnant. While we may be a long way off an all-German final, there is every reason to applaud Goerges route to the semi-final.
Once Williams had figured out how to break the Giorgi serve, though, in the fourth game of the second set, the momentum changed. "I mean, I'm hoping this is, like, a new thing", she said. "But I felt good". It's 5-3 for Kerber and she will once again be serving for the match.
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.
Germany's Julia Goerges apologised after beating close friend Kiki Bertens to progress to the first semi-final of her career at Wimbledon.
After a series of upsets made this edition of Wimbledon the first since it began seeding players in the 1920s that none of the top 10 women reached the quarterfinals, Nos. Sometimes I feel I can fight. For the first time at this year's Wimbledon, she had lost a set.
Elena Ostapenko their way into the semi-final took the match with the former fourth racket of the world Dominika Cibulkova. "I feel like I'm back, but I still have a long way to go to get to where I was". "It's an honour to share the court with her", Goerges said after booking her last-four spot. She won 44 of the last 54 points she served.
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