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World number one and defending champion Williams overcame a mid-match wobble to see off 11th seed Ana Ivanovic 6-1 3-6 6-1 in a clash featuring two notable shifts in momentum.
And she will face Errani, who claimed a 6-3 7-5 success against Jelena Jankovic earlier in the day to keep alive her hopes of becoming the first Italian winner of the event since Raffaella Reggi in 1985.
Williams appeared likely to cruise into the final when she reeled off five games in succession to wrap up the opening set with a minimum of fuss.
Yet, to her credit, Ivanovic responded superbly, winning the first four games of set two before overcoming a momentary lapse to level the match.
Seemingly stirred into life by her opponent's recovery, Williams upped the ante in the decider.
Ivanovic had no answer as the American moved 5-0 ahead before going on to serve out the match at the first attempt.
Errani made a poor start to the day's opening semi-final, dropping her second service game.
However, the world number 11 bounced back to claim the next four games on her way to going a set in front.
The second set followed a similar pattern, as Errani once again found herself a break down early on but recovered well to outnumber her opponent by three breaks to two and book her place in Sunday's final.