Svitolina, the Ukrainian heroine who was a wildcard entrant having only returned to the circuit three months ago, won 7-5 6-7 (5-7) 6-2 in nine minutes under three hours in Tuesday's quarter-final.
Fuelled by emotion and roared on by Centre Court, Svitolina recovered from blowing 4-1 and 5-3 leads in the second set tie-break to sweep away the reigning US and French Open champion.
Having beaten four grand slam champions so far in Venus Williams, Sofia Kenin, Victoria Azarenka and Swiatek she now faces Marketa Vondrousova, a French Open runner-up in the last-four .
The 24-year-old Czech Vondrousova, who is also unseeded, closed out with five successive games to beat No.4 seed Jessica Pegula 6-4 2-6 6-4, coming from 1-4 down in the final set.
Svitolina, who is living in London and has been supported by British tennis bodies, is married to former French star Gael Monfils and gave birth to their daughter Skai on October 15 last year.
The 28-year-old former world No.3 said after her win: "At the beginning of the tournament, if someone would tell me that I will be in the semi-final and beating world number one, I would just say that they're crazy."
She then had the home crowd laughing by adding of her post-match plans: "First of all, I'm going to have a beer, probably,"
The semi-final will be Svitolina's second at Wimbledon, having lost to eventual champion Simona Halep at that stage in 2019.
Vondrousova has won more matches on grass at this tournament than in her entire career going into Wimbledon, having not previously gone past the second round here.
"It's amazing. I'm just loving grass now," she said.
Pegula, who has now lost six grand slam quarter-finals out of six, was the fourth seeded player Vondrousova has beaten this fortnight.
The American was leading 3-1 in the third set when play was suspended so that the roof over No.1 Court could be closed with rain approaching.
Pegula held serve to lead 4-1 but failed to win another game as her jinx of never being able to get past a grand slam quarter-final in six attempts continued.
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