The 24-year-old advanced to 5-4 and three match points at 40-0.
He decided the match with an ace and was able to unleash the joy of the crowd.
Two successful tiebreaks took the match in Tiafoe's favor.
Tiafoe won the second set tiebreak 7-0.
At 6-0, he put an exquisite stop ball in front of the net and at the closing 7-0, he jumped into a backhand on Rublevs for loose second serve.
While an irritated Rublev argued with the referee, Tiafoe sat in his chair and clenched his right fist as fans cheered in the packed Arthur Ashe Stadium.
- I feel so at home here and you bring out the best in me, says Tiafoe to the audience.
Tiafoe, the son of migrants from Sierre Leone and raised in impoverished circumstances, broke to 4-3 in the third set and nodded his head in delight as the crowd showed their appreciation.
Rublev showed great emotion, threw the racket, scolded himself and tried in every way to turn the match that was slipping away from him.