The 36-year-old Murray, the 2012 US Open champion, went down 6-3, 6-4, 6-1 to Dimitrov, and has not been past the last 32 of a Grand Slam in six years.
The Briton's build-up to the tournament was hampered by an abdominal injury sustained in Toronto earlier this month which forced him to miss the Cincinnati Open.
Former world number three Dimitrov, who saved three match points in the opening round, meets 2020 runner-up Alexander Zverev for a place in the last 16.
"I was expecting honestly five sets in a way, so I was constantly trying to remind myself I was here for the long haul," said Dimitrov, who won a 63-minute first set to take charge of the match.
"We've played multiple times, he's a tremendous competitor. I'm very happy with the fight."
Dimitrov reached the semi-finals in 2019 but had fallen in the second round in each of the past three US Opens.
"I had great memories in 2019. I would love to repeat that and why not go further," he said.
