With her easy power game in sync, Williams looked serene as she cruised to victory to set up a clash with Italy's Camila Giorgi, the fifth unseeded player she will have faced in a dream draw on her Wimbledon return.
"For every single day that I'm here I'm trying to do my best. You can be a mom, you can still play tennis and you can still be great", Williams said afterwards. "I'm just here just to be here and to prove that I'm back. For me, there's so much further I want to go to get back where I was, and hopefully go beyond that". "I still have a long way to go to be where I was".
Goerges, seeded 13th, faces seven-time Wimbledon champion Serena Williams on Thursday for a place in Saturday's final.
Going a break down elicited a typically angry response from Williams, who surged into a 40-0 lead on Giorgi's serve in the subsequent game.
Williams hit six of her seven aces in the final set, including one clocked at 122 miles per hour, and won 44 of the last 54 points she served. "After the first set, I just said, 'Let's go three sets.' I just kept fighting". "Sometimes I feel I can fight".
Not one top-10 seed has made the women's quarterfinals at Wimbledon.
Goerges came back in her match, too, defeating Kiki Bertens 3-6 7-5 6-1 in her first grand slam quarterfinal at about the same time Williams' match ended.More news: Divers Hope To Rescue Remaining Boys Trapped In Thai Cave
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But Pliskova, who reached number one in the rankings after Wimbledon past year, found some fight and capitalised on a loose game by Bertens that allowed her to break back and level the set at 4-4.
Still, Kerber had some trouble closing things out. Kerber served for the victory at 5-4 in the second set but got broken. Giorgi won 84 percent of points on her first serve and nabbed three aces.
She is unbeaten at the championships since 2014, winning the title in 2015 and 2016.
Kasatkina, who earlier this year became the fifth player in WTA history with multiple wins over a WTA No. 1 before her 21st birthday, had 31 unforced errors, including seven double-faults.
In March, she lost in the first round of the Miami Open to Naomi Osaka, leading to a hasty exit in which she bypassed a postmatch media session.
Kerber is a former No. 1 who owns two Grand Slam titles and was the runner-up to Williams at Wimbledon two years ago.
Ostapenko played her usual aggressive style, compiling a 33-6 edge in winners. The number 11 seed overcame a determined Belinda Bencic 6-3, 7-6 and, like Görges, will fancy her chances at upsetting Williams' charge to the title.
Goerges turned out to be an unstoppable force as she won eight of the last nine games to subdue her friend, whose lunging effort on match point rolled into the bottom of the net.