Andreescu, 18, is ranked 152nd in the world.
Rain meant no matches were completed at the Shenzhen Open, with Veronika Kudermetova a set up against Vera Zvonareva and Sorana Cirstea 2-0 ahead in the first set of her clash with Alison Riske before play was suspended.
After beating the world No. 3 Wozniacki in straight sets on Thursday night, Andreescu took her game to another level against Williams on Friday night.
"I believe that anything is possible and tonight I think I did the impossible", Andreescu said. "I knew she was a very tricky player". "It's just such an awesome feeling".
The result would have surprised Williams, who had earlier spoken of how she expected to meet Wozniacki in the quarter-finals.
Andreescu, who is ranked 152 in the world, previously said it was a dream come true to beat Wozniacki. "I tried to stay in the present moment, but at 5-4 in the second set, I really knew I had it then".
"Canada has gone from being a minor nation in tennis", says Roth, "Sure, we've always had a few players who were good, to now being a legitimate force in the tennis world". "I just fought to the end".
Andreescu will face Hsieh Su-wei - a straight-sets victor over Sara Sorribes Tormo - in one semifinal. Andreescu had to earn her way into the ASB Classic by winning the qualifiers.
She will take on the victor of the match between Hsieh Su-wei and Sara Sorribes Tormo in her semi-final.
Bouchard, from Westmount, Que., did post a doubles semifinal win Friday with American Sofia Kenin. Andreescu has dropped two sets: one to Laura Siegemund in the final qualifying round, and one to Venus Williams in the quarterfinals. Before the season ended, however, she won two more Challenger events to build some momentum heading into the new season.
"She's very athletic and she moves well around the court", Branstine said from Orange County, Calif.
"This week I've been playing a lot of different types of game styles".