The ninth-ranked Dimitrov started fast in the first meeting of top-10 seeds in this year's tournament against a frustrated Rublev, who smashed his raccquet against his left hand in the first set, then required medical attention from a trainer.
Dimitrov won the final six points of the second-set tiebreaker before Rublev charged back in the third and fourth sets.
Then, with Serena Williams watching from inside Arthur Ashe Stadium, Dimitrov regained control to reach his eighth grand slam quarter-final with a 6-3 7-6 (7-3) 1-6 3-6 6-3 victory.
The Bulgarian beat Roger Federer in that round in 2019 to match his best result in a major by reaching the semi-finals.
With 23-time grand slam singles champion Williams - a friend who he said talked to him to help him prepare on Saturday - giving him a thumbs-up from her seat after the match, Dimitrov said he loved the atmosphere inside Ashe.
"It brings back such good memories from 2019, so I thought, 'Why not another five-setter?'" Dimitrov said.
He will next face either American world No.20 Frances Tiafoe or Australian 28th seed Alexei Popyrin, who ousted defending champion Novak Djokovic.
American 12th seed Taylor Fritz also made the final eight by beating Norwegian seed Casper Ruud 3-6 6-4 6-3 6-2.
Brandon Nakashima was trying to make that an all-American quarter-final match-up when he played No.4 seed Alexander Zverev later on Sunday.
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