Her progress at Flushing Meadows has already guaranteed her a return to the top five of the world rankings for the first time since 2011. She fell to Caroline Wozniacki past year.
Sevastova beat Maria Sharapova in the fourth round and was trying to reach the first major semifinal of her career. This may finally prove to be her year, beating two seeded players and dispatching Vinci and Barty in straight sets.
The seven-time major champion has overcome injuries and illness in recent years, while Kvitova faces a Grand Slam quarter-final nine months after suffering a knife attack.
Over in the women's singles, there are only two Major winners remaining in the draw.
Kvitova, whose previous five matches against Venus all went to three sets, led early on when a third Williams double fault in the third game put the Czech 2-1 up. "The world we live in is just shocking".
Kvitova's response was excellent. She sprayed a second serve four feet long then failed in her effort to squeeze a forehand down the line, gifting back the break at 15.
Four of those clashes have been won by Kvitova and it was the Czech who seized the initiative in the third, breaking after a series of brilliant backhands. They went to the tie-break. She played very well in the tie-break. "You can't just sit back and hope". "I wasn't trusting in it because I was kind of afraid because I didn't want to fall".
Then came a brief delay to close the roof against some advancing rain, but it did not hold up Kvitova, who aced to hold for 4-1, and she would keep her lead for the set, 6-3.
"I'm glad I'm still able to compete on the high level against the top players which I hope will give me some confidence to continue to play well, to know that it's still there somewhere", Kvitova said.
Williams paid tribute to her beaten foe too.
"What she has gone through is unimaginable, unreasonable", Williams said. "Of course that's why I'm playing tennis, and that's why I wanted to be back and playing, and it is a big motivation".
"I try to tell myself to enjoy the competition and enjoy the battle and I think I was able to do that tonight".