"Actually, I thought about it when I lost the first set and I was like, "Oh, my God, I'm never going to say this again", she added with a grin.
Svitolina could rise three spots to world number four on the rankings after her triumph and she has now won nine straight finals.
Kerber plays the unbeaten Stephens in the last round-robin match from Red Group, with the victor joining Bertens in the semi-finals.
Svitolina fell onto her back on the court in celebration, and then shared a hug with Stephens.
2018 marks the first season she has reached four finals in a year, at Miami, Roland Garros, Montreal and now the WTA Finals (she previously reached three in 2016, at Auckland, Acapulco, Charleston, winning all three).
"In the end, it was just about running and chasing every ball. the level was very tough, we were both playing such good tennis, I was just happy to close it out", Svitolina said in a post-match interview.
Svitolina outlasted the world number nine 7-5, 6-7 (5/7), 6-4 in two hours and 39 minutes to continue her bid to make amends for a lacklustre early exit previous year. It's been awesome to play against her here and, of course, I want to thank the crowd.
The American, forced to the first deuce game of the match, saved a couple of break points. The Ukrainian had two opportunities to break Stephens' serve in the next game, but the latter saved the first break point with a forehand victor down the line and the second with a backhand cross-court victor.
Naomi Osaka has set her sights on becoming better on different surfaces, as the US Open champion's season ended in tears at the WTA Finals on Friday.
Svitolina arrived in Singapore out of form yet determined to "silence the haters", who she said believed she did not deserve to be in the tournament, and the Ukrainian has played brilliantly to win all three pool matches and her semi-final.
Stephens' blistering forehand dictated, as she ran away with the first set.
But she gave the break back with a final miss on the third opportunity in the very next game. Nothing's working. But then I won one game.
In the second, the big difference was Stephens' unforced errors (18 to 6): spurred by her opponent's inconsistency, Svitolina went 3 for 4 on break points.
The American impressively counterattacked and pinpointed the lines to frustrate Kerber, who survived an injury scare when she landed awkwardly midway through the first set.
"It is unbelievable. I am very pleased with my performance this week", said Svitolina, who has won her past nine finals on the WTA Tour and not lost one in the last two seasons.