Andreescu, who entered No. 152 in world rankings and had to go through qualifying just to get in, put together some spectacular upsets on her way to the final in the tune-up event for the Australian Open.
"I believe that anything is possible, and tonight I did the impossible", Andreescu said in her post-match interview.
"I really don't want to think about (winning) but it's hard not to". "I'm really just speechless".
"I've had a couple of back issues the past couple of months". I've no idea how.
Andreescu played herself to a standstill, keeping rallies alive with a mix of well-angled strokes from the baseline and delicate drop shots until Wozniacki made mistakes.
Georges clinched the second set in 45 minutes with a pivotal break in the 11th game, then took the deciding third set in only 23 minutes as Andreescu exhausted in her eighth match at the tournament.
But the Canadian teen immediately broke again and held serve for the set before breaking Wozniacki twice in the second set.
The come-from-behind victory came a day after she eliminated top seed and world No. 3 Caroline Wozniacki.
"That'll be a great match up".
The match was a topsy-turvy affair, with the Canadian's impressive variety and depth on her groundstrokes giving the 37-year-old Williams - who is over twice Andreescu's age - everything she could handle.
Williams, seeded six in Auckland, broke Davis for the first time in the sixth game of the first set and took control from there.
But the 30-year-old Goerges was the more assured player in the tiebreak, and converted her third match point to seal the match. At 17, Anisimova is the youngest player in the top 100.
Bouchard did win a doubles semifinal on Friday, teaming with American Sofia Kenin to beat No. 4 seeds China's Xinyun Han and Croatia's Darija Jurak 6-7 (5), 6-4, 10-8.