Slovakian third seed Cibulkova shook off the memory of four prior defeats against Radwanska, including a 6-0, 6-0 thrashing in the final at Sydney in January, to claim a third career WTA title.
She broke world number four Radwanska for a 5-4 lead in the third set, then clawed through a final game lasting more than 10 minutes to seal the triumph on her fifth match point.
"It seemed like forever," Cibulkova said of the final game, but she was beaming after firing a backhand winner to take the match, her father, Milan, racing onto the court to congratulate her moments after.
"He got a little emotional," said Cibulkova, who had done a good job of controlling her own nerves as the match points piled up in the final game.
"When I missed the first match point, I was like 'No way'. Then it was second, third, she had a break point to come back. It wasn't easy," the 25th-ranked Cibulkova said.
"That's why I'm really proud I got this win."
Cibulkova, who admitted that the crushing defeat in Sydney had stuck with her for some time, said she was relieved to open the match by holding serve.
But it was Radwanska who led after the first frame, courtesy of two service breaks.
Cibulkova got her booming forehand working in the second set to level the match, and refused to fold even after falling behind 2-4 in the third.
All of Cibulkova's WTA titles have come in elite Premier level events, including at Moscow in 2011 and Carlsbad -- down the coast in California -- last year.