Before the US Open, Evans had failed to win two successive matches on the ATP Tour this year.
But after beating Khachanov in five hours and 35 minutes, he moved past Argentina’s Mariano Navone in straight sets in the second round.
However, the fatigue appeared to catch up with him on Louis Armstrong Stadium as his impressive run at Flushing Meadows petered out in disappointing fashion.
Evans was looking increasingly weary when he found himself serving for the second set after breaking at 4-4.
But he failed to see the job through, and used valuable energy to win the resulting tie-break.
That effort appeared to cost him dearly in the third set as he required medical attention for an issue with his hip.
With nothing left to give, Evans was jeered by some of the crowd as De Minaur sped through the fourth set in 18 minutes, dropping just two points.
“The irony of it [being booed] is that I was staying on the court for them, but I’ve had worse, I’ll survive,” said Evans.
However, many fans recognised the Briton’s achievement in winning the longest match in US Open history and he left the stadium to a standing ovation.
Evans added: “It’s been a long week. I played good tennis today and unfortunately my hip was problematic in the end but I leave with fond memories of New York for another year.”