Pliskova had strapping on her lower right leg but moved well against the sluggish second seed. The Czech closed out the match on a third match point with an ace. "So, yeah, until the next match, I can really enjoy this win", she said. "From the beginning you have tough matches and even if you don't start well, you are still alive and fighting for a semi-final spot", Svitolina added.
Pliskova played down injury concerns.
"I mean, this win definitely now I want to take, you know, as one to go forward, and for all those people and haters that were saying that I don't deserve to be here and I'm not good".
Kvitova, meanwhile, remained upbeat despite her loss, as she has two more matches in the round-robin stage to revive her hopes of advancing to the semi-finals.
The world number eight stunned Wozniacki with a brilliant first set highlighted by trademark booming ground strokes.
Kvitova, meanwhile, relies on her booming forehand to put pressure on her opponents but the left-handed Czech racked up a plethora of unforced errors and double faults to gift the opening set to an increasingly-confident Svitolina.
The two groups for the lucrative season-ending competition were drawn on Friday at a glitzy ceremony in Singapore, which is hosting the event for the last time.
"I remember 10 years ago as a kid, I was coming here just to watch this tournament and I was dreaming of just standing on this centre court holding the trophy and here I am, it's a dream come true", said Kasatkina.
"She served pretty well in those times, as well, but I think that she really played very consistent".
The Dane started to find her groove but squandered break points in the eighth and 10th games in a disappointing start to her title defence.
The world No 3 was beaten 6-2 6-4 in one hour and 34 minutes by the Czech, who Wozniacki overcame in the semi-finals previous year. The Dane drew two-time Wimbledon victor Petra Kvitova as her highest seeded rival in the White Group.
Svitolina had won just one set in seven straight harrowing defeats to the Czech but impressively turned the tables.
"I would be more sad if I would be preparing to play Singapore and then not got in. I was really, really solid, and I think this was really the key".
In the earlier match, Svitolina capitalised on an error-prone performance by Kvitova to emerge victorious. Throughout the first set the Ukrainian looked the more adventurous while Kvitova seemed to take a while to warm up to the supposedly faster conditions.
Svitolina broke in the sixth game and held her nerve to claim just her second victory against Kvitova from nine meetings.