Third seed Hsieh defeated world No. 86 Sara Sorribes Tormo 6-3, 6-2 in 1 hour, 17 minutes in the quarter-finals. An injury-marred 2018 saw the young Canadian consolidate her Top 200 position with a 43-18 win-loss record in ITF tournaments and WTA qualifying, but she fell in the final round of qualifying at both Roland Garros and Wimbledon - the closest she came to a WTA-level main draw past year.
A day after knocking out world No 3 Caroline Wozniacki of Denmark, 18-year-old Andreescu put on another stunning display to oust 2015 Auckland champion Williams.
But that certainly couldn't be said of Andreescu, who's beat the No 1, 6 and 3 seeds in her past three matches and also come through the qualifying draw.
From there the young Canadian reeled off 11 games in a row before a Williams rally briefly prolonged the deciding set.
She'll face defending champ Julia Goerges of Germany in tomorrow's final.
Despite the distraction of blustery wind, Bouchard seemed headed for an upset over the tournament second seed when she won the first set.
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United will now move on to much tougher challenges, starting with the Premier League visit to Tottenham a week on Sunday.
The 14th-ranked Goerges downed the 87th-ranked Canadian 3-6, 6-3, 7-6 (6). "So for me it's not about giving up, it's about finding solutions and trying to find a way to get a victor".
Andreescu will meet Venus Williams after the seven-time major victor overcame Lauren Davis 6-4 6-3, while Amanda Anisimova will meet Viktoria Kuzmova after they beat Barbora Strycova and Sofia Kenin respectively.
On Saturday, she took charge of her match with Hsieh from the outset, producing the range of drop shots and changes of pace which have served her so well this week but playing with more obvious confidence.
"I'm 6-1 and a foot taller than her but she hits it just as hard so I had to be on my toes".
She then lost two straight games but broke her opponent for the set.
"I guess Auckland brings out the best in me".