The scores were 6-2, 1-6, 7-6 (7-4).
The 18-year-old Radwanska was on the verge of defeat in the final set tiebreaker, but held serve when Craybas, 33, made a huge error on a backhand shot at 5-6.
"I was nervous and everything was upsetting me," she said. "But I was also fighting until the last point and was very relieved when I finally won it."
Radwanska's second career WTA singles crown was worth a first prize of $25,650.
Craybasm fell to 1-1 in WTA tournament finals.
She won the Japan Open at Tokyo in October 2002.
"I'm disappointed I lost but it was a great week and I'm going to take all the positives from it," Craybas said.
Notable deaths of 2014 [PHOTOS]