Svitolina, the world number four, was already eliminated after losing her first two matches but she took Halep down with her as she won 6-3, 6-4 in 71 minutes.
Halep needed victory to keep her campaign alive but the Romanian struggled to click into gear against a relaxed Svitolina at the Singapore Indoor Stadium.
It means Garcia, the lowest-ranked player in the draw, tops Red Group and will play Venus Williams on Saturday, while Caroline Wozniacki will face Karolina Pliskova in the other semi-final.
Svitolina went for her shots and dictated from the back of the court, rattling a shaky Halep, who had suffered a big loss to Wozniacki in her previous match.
“I played free it was a good match for me and I am very happy to finish in Singapore with the win,” the Ukrainian said.
Svitolina dictated from the start, breaking Halep’s tentative serve straight away and winning the opening three games before claiming the first set in 31 minutes.
Halep fought back in the second set with an early break but she was broken straight back and her head dropped when Svitolina claimed what turned out to be the decisive break in game seven.
Even though she endured disappointment in Singapore, Halep will finish the year as world number one if Pliskova does not lift the trophy on Sunday.
— WTA (@WTA) October 27, 2017
Earlier Garcia, the world number eight, admitted it felt surreal even to be in the tournament after her thrilling 0-6, 6-3, 7-5 victory over Denmark’s Wozniacki.
Garcia, who won her last two tournaments to reach the Finals, was two points from elimination in the 10th game of the third set but she dug deep to hand Wozniacki her first defeat of the competition.
Even so, Garcia had to endure a nervy wait until Svitolina beat Halep to send her into the last four. The Frenchwoman lost to Halep but then beat Svitolina in her earlier matches.
“It was kind of weird, actually, to be here. I mean, I qualified last minute, two weeks before. I wanted to keep improving like I did. That’s why I think I won these two matches,” Garcia said.
Wozniacki, who has been in sensational form in Singapore, described her first loss as “annoying”.
“I feel like I should have won that match, but it is what it is,” she said. “I had the chance to serve it out and I didn’t. That’s really it.”
Wozniacki seemed headed for a third straight victory after dominating in the early stages through controlled aggression off the baseline, precise counter-punching and clutch serving.
The 27-year-old had just one unforced error in an almost flawless first set lasting just 22 minutes.
But the match took an unexpected turn in the second set when Wozniacki had a time violation and argued with the umpire during the third game.
Garcia capitalised and won four straight games en route to levelling the match, before outlasting Wozniacki in a tense third set to register her first win in their three career meetings.
Magnus Norman ended his four-year spell as Stan Wawrinka’s coach on Wednesday, after a partnership that saw the Swiss win three Grand Slam titles.
Swede Norman joined up with Wawrinka, who is sitting out the rest of this season with a knee injury, in April 2013 and helped him become one of the top players in the men’s game, but has decided to take a break from full-time coaching.
“After much thought I have decided to dedicate my future to my family. With two young kids at home, now is the right time for me to be with them,” Norman said in a statement.
“I could not have had a better player to work with and this has been one of the most difficult decisions I have ever had to make.
“I’m really honoured to have worked with Stan who is a great tennis player, but more importantly a fantastic person. I wanna thank the whole team behind Stan for all the work over the last four years. It’s been a teamwork and a privilege from the first day.”
Wawrinka, 32, was the world number 17 and had never reached a Grand Slam semi-final before he worked with Norman but has since reached the last four at major tournaments nine times, most recently when he lost the French Open final to Rafael Nadal in June.
“I would like to thank Magnus for the amazing four years we had together,” said Wawrinka, who will return from his injury layoff this December at the Mubadala World Tennis Championship in Abu Dhabi.
“I will always be grateful for the work and the time he spent on me to make me improve and become a three-time Grand Slam Champion. He was not only part of my team but also part of the family.
“For now I’m focusing on my rehabilitation and I will take time to decide with my team the necessary next steps.”
Roger Federer thrashed American teenager Frances Tiafoe 6-1, 6-3 on Tuesday as the top seed began his week at the Swiss Indoors with a resounding first-round victory.
The 36-year-old Swiss, who has competed in a dozen Basel finals, made quick work of his 19-year-old opponent, who had taken him to five sets in this year’s US Open first round.
Federer will next face France’s Benoit Paire, a 6-3, 7-6 (4) winner over American Steve Johnson.
“I felt good throughout. The short match didn’t matter too much because I have a day off tomorrow. Even if it had been three sets, it would have been OK,” Federer said.
“As long as I’m winning, it’s all good. I’m just happy to win the first match. Frances was tough in the US Open.
“The next round with Paire will be tough, he’s a dangerous player indoors. I’m happy I’ve found my rhythm early in Basel.”
— Tennis TV (@TennisTV) October 24, 2017
As a result of his loss, Tiafoe was knocked out of the points race to the inaugural edition of the Next Gen Finals in Milan, reserved for players under 21.
Two more seeds joined Federer in the second round, with number three David Goffin defeating German Peter Gojowczyk 6-2, 7-5, and fifth seed Jack Sock of the US rallying past Canadian Vasek Pospisil 3-6, 7-6 (9/7), 7-5.
Argentine Leonardo Mayer knocked out number eight seed Mischa Zverev 7-5, 7-5.
Against Tiafoe, whom he also defeated last March in Miami, Federer wasted no time in establishing domination of the young gun.
The Swiss quickly rolled 4-0 ahead, with Tiafoe finally earning a game after 21 minutes of play.
Federer then produced a love game and closed out the set in 29 minutes on his first set point.
Tiafoe’s resistance stiffened slightly in the second set, with Federer achieving the break in the eighth game for 5-3 before wrapping up victory in 61 minutes.