Third seed Alexandrova claimed a comfortable 6-1 7-5 win in 80 minutes to setup a meeting with Clara Burel, who clinched a surprise 6-3 6-1 win over Varvara Gracheva despite being ranked 56 places below her opponent.
Kristyna Pliskova was knocked out following a hard-fought 7-5 6-4 loss to Alize Cornet.
Cornet's reward is a tie with eighth seed Magda Linette, who triumphed 6-2 6-0 in a one-sided match against Nao Hibino.
Top seed Halep, playing her first tournament since the resumption of the season, took less than an hour to wrap up a crushing 6-2 6-0 victory.
The two-time grand slam champion came through three-set contests with Polona Hercog and Barbora Krejcikova en route to the last eight, but had no such trouble in a one-sided quarter-final.
Halep broke three times in each set as lucky loser Frech, playing her sixth match of the week, was blown away by the Wimbledon champion.
The world number two, yet to confirm if she will play in the upcoming US Open, said: "The whole game was better today.
"I'm happy that I can play better and better day by day. It was a good one and I'll take it."
Halep will either face fellow Romanian Irina-Camelia Begu or Sara Sorribes Tormo for a place in the final, with the latter having taken the first set of their quarter-final before play was suspended due to rain.
Third seed Elise Mertens earlier overcame wildcard Eugenie Bouchard 6-4 1-6 6-4 and will take on Kristyna Pliskova, who advanced when Ana Bogdan retired due to injury when leading 5-2 in the first set.
World number two Halep claimed a 7-6 (7-2) 6-3 victory in the Czech capital and has the chance to extend her winning streak to nine matches having won the Dubai Duty Free Tennis Championships in February before the WTA Tour's suspension for the coronavirus pandemic.
Begu deserves immense credit, though, having spent seven hours on court over her first three matches and having to conclude a three-set quarter-final triumph over Sara Sorribes Tormo earlier in the day with rain having delayed the match.
"I didn't play my best tennis but also she was tired, so in my opinion, it was a good match," Halep said in her on-court interview.
"I'm really happy that I could win it. It's always tough to play against her. She's a great player."
Awaiting in Sunday's final is third seed Elise Mertens, who defeated former finalist Kristyna Pliskova 7-5 7-6 (7-4) in the day's earlier last-four contest.
World number 69 Pliskova struck 28 winners to 13 unforced errors on home soil as she secured a 6-1 7-5 victory in one hour and 22 minutes.
The Czech wrapped up the opening set in just 21 minutes and Martic paid the price for passing up two opportunities to hold serve at 5-5 in the second.
Pliskova, a runner-up in Prague in 2017, made Martic pay by serving out the match and setting up a meeting with Ana Bogdan, who got a walkover after Lesia Tsurenko withdrew prior to their match.
Mertens ensured Simona Halep is not the only seed remaining in the draw by defeating Camila Giorgi 6-4 6-2, while, in matches held over from Tuesday, Laura Siegemund and Tamara Zidansek wasted little time in wrapping up three-set victories over Mayar Sherif and Katerina Siniakova respectively.
It was not a day off for Halep, though. The Romanian joined forces with Barbora Strycova for a doubles match against Veronika Kudermetova and Anastasia Pavlyuchenkova that ended in a 6-3 3-6 10-8 loss.
Williams needed two hours to overcome compatriot Christina McHale 3-6 6-2 6-3 amid blustery conditions, dropping four of the first five games before hitting her stride.
"I got myself in a hole and I was able to get out of it, so that was satisfying," said Williams, who will face Laura Siegemund in the quarter-finals after the experienced German similarly beat Coco Gauff in three sets.
"I just got mad, and honestly, I said that I wanted to win more than one match here in New Zealand. I thought about that and sometimes it's the craziest things that get you motivated."
Caroline Wozniacki, who is into the doubles semi-finals as Williams' partner in Auckland, came through a topsy-turvy encounter to beat Lauren Davis 6-1 4-6 6-4.
A dominant opening set from Wozniacki, where Davis was unable to hold serve, was not indicative of the absorbing back-and-forth that followed.
"I got a little lucky in the end and it could have gone both ways," the 29-year-old, who will retire after Melbourne, said.
Julia Goerges is up next for Wozniacki and enjoyed a more straightforward 6-3 6-2 win over Jil Teichmann.
World number one Ash Barty's first singles match of 2020 ended with American qualifier Jennifer Brady prevailing 6-4 7-6 (7-4) at the Brisbane International, where Osaka was facing a similar fate after dropping a tie-break in the opener of her match against Sofia Kenin.
The defending Australian Open champion stormed back to take the contest 6-7 (3-7) 6-3 6-1 and will face Kiki Bertens – a 6-3 2-6 7-5 winner over Anett Kontaveit.
Petra Kvitova made light work of Liudmila Samsonova, dropping only five games in a straight-sets victory, while number two seed Karolina Pliskova sowed more disappointment for the home crowd by beating Ajla Tomljanovic 6-4 6-7 (5-7) 6-1 to set up a quarter-final against Alison Riske.
Pliskova's twin Kristyna rounded out the quarter-final action at the Shenzhen Open with a 6-4 6-4 win against Kateryna Bondarenko.
She will face Elena Rybakina, who beat third seed Elise Mertens 6-4 4-6 6-2, while Garbine Muguruza and Ekaterina Alexandrova came through three-setters against Zarina Diyas and Wang Qiang respectively to reach the other semi-final.