World No. 1 Victoria Azarenka will meet Maria Sharapova in Friday's opening semifinal, after which Williams will attempt to continue her recent domination of women's tennis.
Williams won Wimbledon and the Olympics along with a tournament in California during a stretch of almost three months in which she has lost only one match. She has not lost a set at the U.S. Open.
She won the first of her three Open titles 13 years ago and will be trying for her second consecutive Grand Slam championship.
Williams has won her only three meetings with Errani, the last one coming three years ago in Dubai.
Azarenka and Sharapova have already faced each other three times this year with Azarenka having won two of those matches. Azarenka has a 5-4 career edge over Sharapova.
They will play for the championship against Andrea Hlavackova and Lucie Hradecka.