The Polish number nine seed lost the first two games of the match but after that dominated proceedings against the world number four in Tokyo.
Zvonareva played an error-strewn game, making 22 unforced errors over the two sets.
"Playing against a player like Vera, you can't worry about tactics," the 22-year-old said after the match.
"I just tried my best from the very first point and stayed focused until the end."
Radwanska's win is her second over Zvonareva this year after defeating the Russian twice in August in the final at Carlsbad and also at the Rogers Cup in Toronto.