The German, who had lost in the first round at the All England Club for the past five years running, prevailed 3-6 7-5 6-1 on No. 1 Court on Tuesday.
She will now face seven-time champion Williams in the last four as the 29-year-old’s pursuit of a maiden grand slam continues.
Goerges, seeded 13th, had to do it the hard way after dropping the first set against an opponent who had prevailed in their previous two meetings.
Despite holding to love to tie the scores at 3-3, Goerges lost the next three games – spurning a break-point opening in the process – to fall behind.
But she dug deep and started to dictate the play early in the second set, adopting an aggressive approach to keep the points brief.
However, having raced into a 4-1 lead, Goerges was promptly pegged back to 4-4 as Bertens again demonstrated the kind of form that had seen her account for the likes of Venus Williams and Karolina Pliskova at this tournament.
Set-point openings came and went for Goerges at 5-4, but Bertens flinched when she next served to stay in the set.
The decider was a one-sided affair, with a tiring Bertens struggling for accuracy off both wings as Goerges raced through to the semis, to her own apparent disbelief.
STATISTICAL BREAKDOWN Goerges [13] bt Bertens [20] 3-6 7-5 6-1
WINNERS/UNFORCED ERRORSGoerges - 36/21Bertens - 19/27
ACES/DOUBLE FAULTS Goerges - 3/3 Bertens - 1/4
BREAK POINTS WON Goerges - 4/12Bertens - 2/4
FIRST SERVE PERCENTAGE Goerges - 49Bertens - 59
PERCENTAGE OF POINTS WON ON FIRST/SECOND SERVEGoerges - 72/68Bertens - 63/42
TOTAL POINTS Goerges - 103Bertens - 82
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