Garcia was in tears at a set and a break down as she let out all her emotions to her dad, who is also her coach, on court.
The French star, seeded eighth for the tournament, knew defeat in Singapore would spell the end for the season – but she charged back to take the set to take it into a decider.
WTA FINALS RESULTS: LATEST SCORES FROM SINGAPORE
Although the rollercoaster contest took another turn as Garcia was twice broken in the third set and Svitolina had the chance to serve the match out at 5-4.
Except the 23-year-old fluffed her line. She went into her shell, Garcia pulled off a string of winners to stay in the match, before holding and breaking the Ukrainian to complete a memorable win.
It’s her first at the WTA Finals and keeps alive her dream of winning the end-of-season tournament.
Earlier in the Red group, Caroline Wozniacki dispatched Simona Halep 6-0 6-2 to make it two wins from two.
The Dane is all but guaranteed a spot in the semis while the remaining one will be taken by the winner of Halep vs Garcia on Friday.
Svitolina, meanwhile, is technically still in the competition but she needs a miracle – and a routing of Wozniacki – to qualify.
It’s the second time in a matter of weeks that Garcia has come from behind to beat Svitolina, who was made to pay for her tentative approach at the back end of sets.
Garcia now leads the head-to-head between the pair 2-1.