Murray, playing some of his best tennis in years recently, could not match Dimitrov's firepower as he struck 16 winners compared to 32 from the 19th seed.
Dimitrov will next face German Alexander Zverev (26), who beat his compatriot Daniel Altmaier (24) 7-6, 3-6, 6-4, 6-3.
Murray made a slow start as Dimitrov broke him to love in the second game but showed resolve when he broke back at the third attempt in an epic 16-minute game.
Dimitrov, however, broke Murray to love in the eighth game and again with a well-placed forehand winner in the opening game of the second set.
Murray, US Open champion in 2012, trailed by a break in the third set when Dimitrov saved two break points and the Bulgarian broke again to close on victory which he secured when his opponent double faulted.
Check out the game summary with Flashscore.
Draper downs Hurkacz
But it was not all bad news for Britain as a dominant Jack Draper (21) upset 17th seed Hubert Hurkacz (26) 6-2, 6-4, 7-5 and Katie Boulter (27) bounced back to beat Chinese qualifier Yafan Wang (29) 5-7, 6-1, 6-4.
Draper dropped down the rankings this year compared to 2022 but said he is playing a more "complete" tennis and was grateful to be at Flushing Meadows after he retired from the Winston-Salem tune-up event due to injury.
"There was maybe a 70/30 chance that I wouldn't play this week. So very, very happy with the fact that I have been able to get out there and play," he told reporters.
"It's weird how sort of this sport works. Sometimes you can be at your lowest point and then all of a sudden, you get on a bit of form and you're playing great and body feels good."
