Cibulkova had lost each of her four previous matches against world number four Agnieszka Radwanska, with the last of those a 6-0 6-0 trouncing in the Sydney final at the start of the year.
But she fought back gutsily in their fifth meeting to post a 3-6 6-4 6-4 victory, clinching the title after two and a half hours on court with a powerful backhand winner on her fifth championship point.
It had looked set to be Radwanska's title when she led 4-2 and 40-15 in the deciding set, but from that point her fellow 24-year-old Cibulkova dominated.
Radwanska was targeting her third title in 2013, and in the absence of Williams Poland's world number four was the top seed this week. Yet third seed Cibulkova, who began her week at 25th in the rankings, refused to let Radwanska impose herself on the contest.
The match began well enough for Radwanska who seized on her two break chances to take the opening set, but there was a twist when Cibulkova broke to lead 4-3 in the second. Radwanska could not recover the break so they went into the decider.
Radwanska broke to lead 3-1 but Cibulkova hit back, only to then give her serve away for a second time in the set.
At 4-2 and 40-15, Radwanska looked almost home and dry, but she allowed Cibulkova back into the game, as serve was broken for a fourth consecutive game.
It was soon 4-4, and Cibulkova forced deuce against the Radwanska serve to heap pressure on the pre-match firm favourite.
A scorching return of serve had brought her deuce, and a similarly unplayable cross-court forehand gave Cibulkova the ninth game, and the chance to serve for the match.
Cibulkova let three championship points slip away before Radwanska engineered a break-back opening, which also was spurned as she pushed a limp forehand into the net.
At the fourth time of asking on championship point, Cibulkova lost a marathon rally to a Radwanska volley, but that fifth chance was just around the corner. This time she got over the line, ending a tense rally by ripping the fierce backhand that raced beyond her opponent's defences.