Petrova, currently ranked 18th in the world, began the encounter the brighter of the two players with a string of forehand strokes that Radwanska was unable to return.
Russian Petrova eventually served out to claim a bagel 6-0 with just under 30 minutes played.
World number three Radwanska responded positively in the second set, dropping just one game on her way to levelling up proceedings, thus forcing a deciding set for the title.
An early break of Radwanska's serve handed 30-year-old Petrova the advantage in the third set.
She then proceeded to hold her remaining service games and as a result claimed her second title of the year.
Despite the defeat, Poland's Radwanska has secured her place in the end of season WTA Tour finals.