Williams, seeded six in Auckland, broke Davis for the first time in the sixth game of the first set and took control from there.
Andreescu admitted to feeling the affects of an emotional week as she enters her first WTA final.
Goerges beat the world No 50, Slovakian Viktoria Kuzmova, 6-1 7-6 (6) before Andreescu beat Hsieh Su-Wei of Taiwan 6-3 6-3. "But I'm just trying to stay grounded right now, stay humble, and use it to my advantage".
Germany's Goerges needed to save match-points in her 3-6, 6-3, 7-6 (6) win over Canadian Bouchard, coming back from a set down and then a match point down at 5-6 in the final set to reel off three successive points and win the encounter in the Auckland Open.
In addition, the match will be Andreescu's first-ever WTA-level championship match, with a victory guaranteed to put her into the top 100 in the world rankings.
"I believe anything is possible", said Andreescu, after her win, "and tonight I did the impossible". "Last year I was so close, and so upset in the beginning when I did not make it, but this year I'm going to do my best, even better than last year".
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Still just 20, Kuzmova began to steady herself at the start of the second. Goerges had two match points at 6-4 but blew both of them with some poor tennis.
"In the second set I stepped away a bit from my line and I wasn't as aggressive as I wanted to be, because in the first set she was behind the baseline and I was more in the court".
"Everybody deserves their spot in the final, so she has played some terrific tennis", Goerges said.
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. Today she didn't serve as well as other matches I've seen her play.