The Polish player came through 7-6(1) 7-5 after two hours and two minutes of tennis.
In an evenly-matched opening set, both players broke serve on five occasions to take it to a tie-break, which Radwanska went on to claim 7-1.
The world number four made an early breakthrough in the second set, breaking Errani in the first game on her way to opening up a 3-1 lead.
Radwanska had the opportunity to serve for the match at 5-4, but Errani levelled matters with a timely break.
However, Radwanska responded by breaking the Errani serve once more before serving out the match 7-5.