The Russian looked down and out after he lost the second set 6-1 to go two sets down, but produced a remarkable recovery to win through 6-7 (5-7), 1-6, 6-3, 6-2, 6-3 in the fifth set and keep alive his bid for a first U.S. Open crown.
Semi-finalist last year, Kafelnikov cut a forlorn figure when he lost the second set 6-1, but he somehow turned the match around.
A total of 29 unforced errors came from Kafelnikov's racquet in the opening two sets, but he tightened up his game to reduce the tally to just 20 in the final three sets as Stanoytchev's early supremacy faded.
As Kafelnikov rallied, so Stanoytchev began to struggle, with his serve proving more and more vulnerable the longer the match went on.
The Russian, seeded five and many people's fancy for the title, took the third set 6-3 in 30 minutes and raced through the fourth to level the match.
the fifth, Stanoytchev lifted his game once more, but Kafelnikov wasn't to be
denied and he took it 6-3 in two hours and 45 minutes to set up a clash with
Alexander Popp of Germany, who beat Jiri Vanek in round one.