The British number two was powerless to prevent five-time winner Federer marching into round four 6-2 6-2 6-1.
In two previous meetings with Federer Evans had not won a set, but he did take the Swiss great to two tie-breaks at the Australian Open in January.
There was also the fact that Federer had made slow starts to his previous two matches, dropping the opening set in both to players far less adept than Evans, to cling on to.
But there was no such luck for Evans. The 29-year-old had to save three break points for 2-2 in the first set, but was then broken twice as Federer whizzed away.
Federer had invited Evans to train with him in the Swiss Alps in April, but he was nothing like as accommodating on Arthur Ashe.
Evans did not win a single point on the Federer serve in the second set as winner after winner – 48 in total throughout the match – fizzed past him.
If the Brit tried to come forward, he was passed. If he stayed behind, he found himself almost pinned to the back wall.
In the third Evans did finally scratch the surface, not only winning three points on the Federer serve but then converting the second of two break points, bringing them level on serve.
It was little more than an act of defiance, Federer breaking straight back to love and running away with the set, wrapping up victory in just one hour and 20 minutes.
"What did I do differently? Nothing," said Federer. "Sometimes you've just got to trust your team, your warm-ups, and everything you've done.
"Maybe Danny wasn't feeling it today, he played yesterday, maybe that was an advantage for me – and I took advantage."