Vinci, the world number 43 and playing her first Grand Slam semi-final, won the American 2-6, 6-4, 6-4 in New York.
While speaking to reporters, she said: “Beating the world number one is like a dream”.
“It’s amazing, like a dream,” she said in her on-court interview.
“I’m in the final. I beat Serena. For me, it’s an amazing moment, incredible, yes.
“For the American people, for Serena, for the Grand Slam, today is my day. Sorry, guys.”
Meanwhile, Serena had needed two wins to complete a clean sweep of all four majors in 2015.
Vinci will play Flavia Pennetta in an all-Italian final at flushing meadows on Saturday.