The 15th-seeded Keys was down a break in the decider against the Ukrainian fourth seed when Svitolina lost her composure and allowed the Florida-based player to come back under the lights on Arthur Ashe Stadium.
"It's gone pretty well so far don't you think," she said on court.
"It's partially thanks to you guys, you helped me when I got down in the third set; You gave me an amazing energy boost."
The last time at least four American women were in the quarter finals at Flushing Meadows was in 2002, with Jennifer Capriati, Lindsay Davenport, Serena and Venus Williams and Monica Seles winning their fourth-round matches.
Jennifer Brady could have been the fifth this year but she was destroyed 6-1 6-0 by world number one Karolina Pliskova earlier on Monday.
Keys joined Coco Vandeweghe, who will meet Pliskova in the last eight, Sloane Stephens and Venus.
Davenport is now Keys's coach and she was seen crying in the stands after her protege hit a backhand winner down the line to seal the victory.
Keys got off to a nervous start as she quickly fell 3-0 behind but once she found her stride, Svitolina was on the back foot and the American forced a tiebreak which she easily won after earning a mini-break with a superb drop volley.
More at ease in the long rallies, Keys was, however, completely overpowered by the big-hitting Svitolina in the second set and the Ukrainian took that momentum into the third.
"I had the feeling I was hitting a wall in the second set," said Keys.
Svitolina broke for 3-2 and held for 4-2 when her nerves got the best of her.
(Reporting by Julien Pretot; Editing by Sudipto Ganguly)
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