Murray, meanwhile, reached at least the quarters at his previous 18 Grand Slam tournaments, a streak that included championships at the US Open in 2012 and Wimbledon in 2013, along with four runner-up finishes. His last loss this soon also happened in New York, in the third round five years ago.
Adept at comebacks - in the second round, he recorded his eighth victory in a match after dropping the opening two sets - Murray did push Anderson to a fourth set, but that was the extent of the rally this time.
Still, Murray kept trying to rile up himself - and his backers - as the fourth set carried on, even reaching over to slap the extended palm of a front-row spectator.
"I was trying to use the energy of the crowd as much as I could to help me," Murray said.
Anderson limited his signs of emotion to one uppercut after winning one point by tracking down a lob and conjuring up a sky-hook winner from the baseline.
And he was perfect at the end, hitting one ace at 135 mph, another at 138 mph, while Murray couldn't get his strokes to land in the right spots.
"I wish," Anderson said, "I could play every tiebreak like that."
In Anderson's first major quarterfinal, he will face yet another two-time major champion, Stan Wawrinka, who eliminated 68th-ranked American Donald Young 6-4, 1-6, 6-3, 6-4.