World number two Radwanska was expected by many to ease past her Italian opponent and into the quarter-finals at Flushing Meadows.
However, Vinci started the brighter of the two players, while Radwanska appeared to be troubled by a shoulder complaint that she has had strapped up throughout the tournament.
Vinci eventually opened up a one-set lead thanks to a 6-1 success.
The second set went with serve until the scores were level at four games apiece. Vinci then struck, winning the next two games to book her place in the final eight.