It was the 30-year-old's second title of the year and the 12th of her career.
"It feels amazing," Petrova said after winning the WTA premier five event, which featured nine of the world's top 10 women.
"It's the biggest tournament I've ever won. I never expected I would be in this position."
Petrova inflicted the dreaded 'bagel' on third seed Radwanska in the first set, taking it with an ace down the middle to rub salt in the wound.
Radwanska quickly turned the tables but Petrova produced some superb tennis in the decider, closing out proceedings with a drive volley before sinking to her knees in delight.
Petrova, who beat top 10 players Sara Errani and Samantha Stosur on her way to the final, enjoyed her best season in 2006 when she won five tournaments.