Earlier, Simona Halep got her campaign off to a perfect start when the Romanian world number four dominated an erratic Madison Keys to kick off round-robin play in the elite eight-woman, season-ending event with a 6-2 6-4 victory.
First-time finalist Cibulkova opened with a double fault and Kerber, who won two grand slam titles in 2016, took advantage of her opponent's nervy start to grab an immediate break without having to do much more than get the ball over the net.
By contrast, the German found her rhythm right away as she located the corners with ease and used her brilliant retrieving skills to make Cibulkova always play an extra shot when it appeared the point had already been won.
The Slovakian, who won her third title of the year in Linz earlier this month, slowly worked her way back into the set with her high-intensity game and pressured Kerber enough to make her cough up two double faults to tie things up at 4-4.
The pair were now slugging it out on the baseline and after both held serve through to a tiebreaker, Kerber kept her nerve in the face of some tremendous pressure to edge ahead in the thrilling encounter.
Undeterred, Cibulkova made a fast start to the second set as Kerber wavered, breaking her opponent twice in a row to race into a 4-0 lead and, while the German threatened to mount a comeback, the seventh seed drew level with a forehand winner.
DOMINANT HALEP
With exhaustion kicking in and the points growing shorter, Kerber recovered after suffering an early break and showed the class befitting the world's top-ranked player to reel off four straight games on her way to a hard-fought victory.
"I was trying to stay focused in the third set, trying to play my game and be aggressive. That was my plan and it worked well... it was a really close and really tough match," Kerber said.
In the opening Red Group match, diminutive Romanian Halep drew first blood in the third game, putting pressure on Keys's backhand side with pinpoint accuracy and converting her fourth break point when the American plonked a weak drive into the net.
Buoyed up by the early breakthrough, Halep went for the kill and rattled off the next 11 points on her way to a decisive 5-1 lead as Keys's game unravelled, riddled with unforced errors.
Keys, on her first visit to Singapore, continued to mix winners with mistakes and, after trading breaks midway through the second set, a fired-up Halep broke again in the ninth game before serving out the contest in a little more than an hour.
"It's always the same with Madison... she's very strong and hits the ball hard so it's tough to match her power," said Halep. "So I have to adjust, be strong with my legs and make the most of my chances."
Defending champion Agnieszka Radwanska opens her campaign against Russia's Svetlana Kuznetsova on Monday with Garbine Muguruza and Karolina Pliskova completing the White Group.
(Editing by Nick Mulvenney and Clare Fallon)
