Vinci, the world number 43 and playing her first Grand Slam semi-final, caused a huge upset with a 2-6 6-4 6-4 win.
Williams, 33, had been two wins from completing a clean sweep of all four majors in 2015.
Vinci, 32, will play Flavia Pennetta in an all-Italian final at Flushing Meadows on Saturday.
Williams’ hopes of winning a first calendar Slam ended just two victories short, and in the most sensational of upsets.
The American had survived 11 final sets in 25 Grand Slam matches during 2015, but at the 12th time of asking came up against an opponent who simply grew stronger.
When Williams smashed her racquet after dropping the second set it was clear that the tension was beginning to boil over, and her cries of “Come on!” in the third set took on an increasingly desperate air.
There was still the possibility that Vinci would crumble in the decider, but she served out to love with two nerveless half-volleys for the win of her life.
“It was an incredible match,’ said the Italian. “I lost the first set, and tried to stay in every point. I tried to stay focused and not think about Serena. It is the best moment of my life.”
Williams remains the holder of all four major titles for another 24 hours, having completed the “Serena Slam” at Wimbledon, but the calendar Slam remains something achieved only by Maureen Connolly (1953), Margaret Court (1970) and Steffi Graf (1988). -BBC