It was the ninth face-to-face meeting between the rivals, in which the Ukrainian won only their second win.
World number eight Stephens has been drawn in the Red Group in Singapore alongside Angelique Kerber, Kiki Bertens and this year's U.S. Open victor Naomi Osaka, who she plays first in round robin action on Monday.
Wozniacki was clearly off her game on the opening night of this year's season-ending tournament as the reigning Australian Open champion found herself chasing the match after she fell behind early.
"It's very nice to be back and I'm very happy with the match and very pleased with the performance", said Svitolina, who completed her victory in 88 minutes with four breaks of service.
"You have other matches you can play and you can continue to, like, learn from the last match you have played".
I didn't think I played badly in the second set and I just had to stay focused. "You need to play at the best level you can imagine because everyone is very strong".
Svitolina tried to interrupt a 4-year series of defeats from Kvitova, numbering seven matches. "If I think that he says something that I don t agree with, then I just do my own thing". Halep plans to take a break to help the herniated disc that ended her season early fully heal and admitted she would not pick up a racket again until at least December.
She started to find her groove but squandered break-points in the eighth and 10th games in a dismal start to her title defence.
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The world number eight stunned Wozniacki with a brilliant first set highlighted by trademark booming ground strokes.
Svitolina set up the second set win by breaking Kvitova's serve to go ahead 4-2.
"Winning this match definitely gives me lots of confidence". If mentally I will be okay and rested, I think it's going to be better.
"I think she started a little bit nervous because it's always tough to defend a title", Pliskova explained in her post-match comments. "I can say I see some players that have a bigger chance, actually Wozniacki because she won a year ago and I think the court suits her".
"Everyone here is a great player and they are here because they had a great season", Kvitova said.
There were signs of nerves from Svitolina as she failed to consolidate the break in the next game, but was undeterred as she took the initiative.
The initial stage of the eight-player WTA Finals field is a round-robin competition with two teams of four players.
But Osaka has a chance to finish a memorable year on a high in Singapore, which starts on Sunday.