Sloane Stephens won 6-1, 0-6, 7-5 in a pulsating match. Venus had been bidding to become the second oldest Grand Slam finalist in the Open era after Martina Navratilova at Wimbledon in 1994.
The 9th seeded 37-year-old was the only member of the quartet who has participated in a Grand Slam singles final. She has won seven major championships, two at the US Open - in 2000 and 2001.
This year was also the first time in the Open era where all the top eight women's seeds at a Grand Slam were eliminated by the quarters or earlier.
Stephens will play Madison Keys, also of the US, in Saturday's final. Keys made it to the final after taking barely an hour to crush CoCo Vandeweghe 6-1 6-2. Both players, who are friends off the court, are hoping to win their first Grand Slam tournament.
Upsets all round
Meanwhile, there will be a first-time men's doubles championship duo after upsets in the semifinals, with fifth-seeded American twins Bob and Mike Bryan stopped in their bid for a sixth title at Flushing Meadows, losing 3-6, 6-3, 6-4 to 11th-seeded Spaniards Feliciano Lopez and Marc Lopez.
The 12th-seeded team of Horia Tecau of Romania and Jean-Julien Rojer of the Netherlands eliminated No. 1-seeded Henri Kontinen of Finland and John Peers of Australia 1-6, 7-6 (5), 7-5.
jbh,es/ng (AFP, AP, Reuters)