Alison Riske of the United States will face Romanian lucky loser Jaqueline Cristian, ranked 100, in Friday's final.
The third-seeded Collins, who is pursuing her third title of the season, beat Alison Van Uytvanck of Belgium 7-5, 6-3.
Raducanu, however, confirmed British media reports that Torben Beltz, 44, who previously coached Angelique Kerber, will take over for next season.
As well as being the first player representing Estonia to make the year-ending championships, Kontaveit is projected to make her Top 10 debut in Monday's rankings.
Halep broke serve six times and saved the only break point she faced in her first service game of the match.
Kostyuk, 19, will play her third semi-final of the season on Saturday, following Abu Dhabi in January and Istanbul in April.
Kremlin Cup 2021: Aryna Sabalenka knocked out by Ekaterina Alexandrova, Maria Sakkari beats Simona Halep
Sabalenka was playing in her first tournament since reaching the semi-finals of the US Open last month. She then missed the tournament in Indian Wells, California, after a positive test for the coronavirus.
The Romanian, who turns 30 on Monday, also reached No 1 in the rankings. She is No 14 this week.
Four-time Grand Slam champion Osaka fell from fifth as Barty remains top and French Open winner Barbora Krejcikova climbed to a career high of fifth.
Day 5 of US Open had its share of fantastic matches and upsets with Tsitsipas, defending champion Osaka and Rublev exiting the tournament.
Fernandez, who won her first WTA title in March at Monterrey, had never beaten so high-ranked a rival as third-rated Osaka and the same was true for Alcaraz when he sent home the men's world number three.
US Open 2021: Stefanos Tsitsipas beats Andy Murray in five-set first-round thriller; Halep, Stephens progress to second round
Tsitsipas defeated the 112th-ranked British star 2-6, 7-6 (9/7), 3-6, 6-3, 6-4 in an atmosphere more like an intense second-week showdown than a curtain-raiser for the fortnight.
US Open 2021 women's singles preview: Ash Barty looking to cap off excellent season, Naomi Osaka to make winning return?
Ahead of the US Open, Firstpost.com takes a look at the women's singles draw and, with equal parts of bravery and naivete, attempts to determine the potential outcome of all four quarters.
Halep only returned to the Tour last week in Montreal, losing in the opening round. She remained confident that progress was not far away after her injury in Rome three months ago.
American Collins extended her win streak to 12 matches - a run that saw her claim back-to-back titles in Palermo and San Jose
Wimbledon 2021: Ashleigh Barty sets sights on Angelique Kerber, Karolina Pliskova preps for Aryna Sabalenka in semis
The stage is set for the women's Wimbledon semi-finals on Thursday with three of the contenders new to the experience.
The 29-year-old Romanian had been battling to be fit since withdrawing from her second round match at the Italian Open in mid-May.
Rafael Nadal, Naomi Osaka and Milos Raonic are the high profile names to opt against playing at Wimbledon which starts 28 June.
Elina Svitolina moves into WTA top 10, French Open champion Barbora Krejcikova slips two places to 17th
Recently crowned French Open champion Barbora Krejcikova slipped two places to 17th while Swiss Belinda Bencic is once again on the cusp of the top ten after her run to the grasscourt final in Berlin.
Elsewhere, third seed Aryna Sabalenka beat fellow Belarusian Aliaksandra Sasnovich 7-5, 6-3 and will next play Anastasia Pavlyuchenkova.