Halep needed to beat the Ukrainian to advance out of her group with Caroline Wozniacki, but went down 6-3 6-4 and will now head home.
Furthermore, she will lose her crown as the world's best if Karolina Pliskova wins the title on Sunday.
Halep's defeat means that in-form Caroline Garcia joins Wozniacki in the final four to carry on her amazing end-of-season run.
Wozniacki fends off Pliskova to reach Singapore final
Garcia, who won back-to-back titles in China to seal a spot at the tournament, was looking dead and buried after losing her first round-robin game against Halep but beat Svitolina on Wednesday and came into Friday's clash with Wozniacki knowing she had to win.
She might have been preparing herself for a flight home after losing the first set to love, but steeled herself against a player who had only dropped four games in her previous two matches and came through 0-6 6-3 7-5.
The Frenchwoman still had a nervous wait to see if she progressed, but after Svitolina, playing with the freedom of a player who already knew she was heading home, was too good for Halep, it meant that Garcia ended up topping the group.
That set up a semi-final against Venus Williams while Pliskova lies in wait for Wozniacki.
Results from the WTA Finals Women's Singles Round Robin Red Group matches on Friday
4-Elina Svitolina (Ukraine) beat 1-Simona Halep (Romania) 6-3 6-4
8-Caroline Garcia (France) beat 6-Caroline Wozniacki (Denmark) 0-6 6-3 7-5
P W L F A Pts
1. Caroline Garcia 3 2 1 4 4 4
2. Caroline Wozniacki 3 2 1 5 2 4
3. Elina Svitolina 3 1 2 3 4 2
4. Simona Halep 3 1 2 2 4 2
1. Karolina Pliskova 3 2 1 4 2 4
2. Venus Williams 3 2 1 4 3 4
3. Garbine Muguruza Blanco 3 1 2 2 4 2
4. Jelena Ostapenko 3 1 2 3 4 2
Garcia overcomes tears to battle past Svitolina
Ruthless Wozniacki turns on style to crush Halep