The 24-year-old Czech, seeded ninth here two months after becoming the first unseeded woman to win at SW19, fell a set behind to Stearns.
But the American youngster, whose powerful forehand accounted for Britain’s Katie Boulter in round three, won just five more games as Vondrousova triumphed 6-7 (3) 6-3 6-2.
“She was playing great from the beginning and I just tried to stay in the game,” said Vondrousova.
“She is a very dangerous player, she has a great future ahead of her and it was a very tough match.
“I’m very happy. I didn’t expect this, after Wimbledon there was a lot of pressure but I’m feeling good and we’ll see what happens next.”
What happens next is a meeting with Madison Keys, a former Flushing Meadows runner-up who sprung a mild surprise against fellow American Jessica Pegula, the third seed.
Keys, seeded 17, is emulating the form which swept her to the final in 2017 and sunk the highly-fancied Pegula 6-1 6-3.
The 28-year-old said: “It’s always tough having to play a friend but we’ve been doing it all our lives. On court it’s all business but then we go back to being friends.”
Iga Swiatek’s surprise defeat on Sunday night means there will be a new women’s champion this year.
But it will not be last year’s runner-up Ons Jabeur after the fifth seed, who has struggled physically all week, bowed out 6-2 6-4 to China’s Qinwen Zheng.