Cibulkova will face either world number one Angelique Kerber or the defending champion Agnieszka Radwanska in Sunday's final
Runner-up at the Australian Open in 2014, Cibulkova will face either world number one Angelique Kerber or the defending champion Agnieszka Radwanska in Sunday's final after defying the odds to book her place in the title match at Singapore's Indoor Stadium.
Voted the WTA's comeback player of the year after slumping to 66th in the world rankings in February, Cibulkova only snuck into the semis on a countback after losing her first two round-robin matches.
She produced another incredible turnaround to win a contest that began slowly but escalated into a nail biter.
"It's just amazing. It's my first time playing the finals. For me it's one of my dreams come true. It's just incredible," Cibulkova said.
"I cannot describe with words how much it means. You work all your life for this, it just feels great."
Cibulkova initially struggled to cope with Kuznetsova's superior power, conceding the opening set after just 33 minutes when she dropped serve three times, once with a ferocious return from the Russian but twice from her own errors, dumping a forehand into the net and hitting another over the baseline.
Cibulkova was much more aggressive with her returns in the second set, and although her nerves got the better of her and she squandered two opportunities to serve it out, she regained her composure and dominated the tiebreaker to force a deciding third set.
There were some anxious moments for the 27-year-old when she lost four games on the trot to trail 4-2 but she dug deep and reeled off the next four games to seal a famous victory that ended Kuznetsova's own fairytale run.
The oldest woman in the elite eight-player field at 31, Kuznetsova had to win the Kremlin Cup in Moscow last week just to qualify for the $7 million event and then won two gruelling three-set encounters to reach the semis.
Battling exhaustion, she lost her final round-robin match against French Open champion Garbine Muguruza on Friday before running out of gas against Cibulkova.