After being broken in the opening game of the second set against Venus, Andreescu reeled off 11 straight games to take control of the match.
The win sees the Canadian reach her maiden WTA semi-final following a hard 2018 campaign marred with injury.
Goerges beat the world No 50, Slovakian Viktoria Kuzmova, 6-1 7-6 (6) in first-up, before Andreescu beat Hsieh Su-Wei of Taiwan 6-3 6-3 to complete the day's play.
"So I remember her always developing and she was always talented, so it's really incredible what she's doing right now".
Goerges is the defending champion and ousted Eugenie Bouchard of Westmount, Que., earlier in the week on her way back to the championship match. But the tide changed late in the second set as Goerges began to put more first serves in play and gain more depth with her ground strokes, forcing the Mississauga, Ont., native onto the defensive.
"I believe that anything is possible, and tonight I did the impossible", Andreescu said in her post-match interview.
Ranked No. 152 in the world, Andreescu beat the top-seeded and former world No. 1 Wozniacki on Thursday before taking out No. 38 Williams, a seven-time Grand Slam champion and also a former world No. 1.
Andreescu's win over Hsieh in a semifinal Saturday was her most dominant performance of the week.
But with the next point she ripped a victor and on her third matchpoint Kuzmova cracked a return straight into the net.
After going up 5-0 in the third and final set, Andreescu let Williams back in the match. "I was still aggressive, but not aggressive as much as I wanted to be".
"For her to make wins like that at such a young age, that's impressive", says Tylek, who is the same age as Andreescu and grew up playing tennis with her.
But Andreescu's relative inexperience certainly didn't show as she used her power game but also showed her own ability to use deft touches to outsmart her opponent.
"This meant a lot", Goerges said.