A well-rested Federer, aided by scheduling that gave Evans only 18 hours between matches, routed the 58th-ranked Englishman 6-2, 6-2, 6-1 in only 80 minutes, blasting 48 winners to just seven for Evans.
"I really enjoyed myself," Federer said. "I was able to adjust and take care of business so it was good."
Evans blasted organizers for playing him first on limited rest after a rain-delayed match on Thursday while his 38-year-old Swiss rival rested after playing Wednesday under the roof at Arthur Ashe Stadium.
"I was fatigued," Evans said. "I thought it was pretty tough I was first up after playing yesterday, if I'm being brutally honest, so it was a bit disappointing.
"Just to try and beat him feeling tired, stiff, playing four sets yesterday, it's near on impossible, but I actually thought he played pretty much no-error tennis."
Five-time US Open champion Federer sympathized with Evans' frustration.
"You could definitely argue the scheduling was not in his favor," Federer said. "It's not fair for me to play my match under the roof, get it done, sit back, relax the next day while he's battling out a three-hour match. That's tennis. It's entertainment and the show must go on.
"I understand if Danny is a little bit frustrated."
Federer bristled at the suggestion he asked for the day match.
"I know there was questions to have a preference, but that doesn't mean like, 'Roger asks, Roger gets,'" said Federer. "Just remember that, because I have heard this shit too often now. I'm sick and tired of it, that apparently I call the shots. The tournament and the TV stations do."
Evans questioned that idea.
"That wouldn't be the first time the higher-ranked player has had pull," Evans said. "The tournament would rather Roger be going through that match than me so it's understandable."
Japanese seventh seed Kei Nishikori was dispatched by the 20-year-old Aussie 6-2, 6-4, 2-6, 6-3. De Minaur will next face Bulgaria's Grigor Dimitrov or Polish lucky loser Kamil Majchrzak.
It was the first victory over a top-10 foe in 11 tries for de Minaur, who squandered a two-set lead over 2014 US Open winner Marin Cilic in last year's Open third round.
"I had a little bit of a thriller last year versus Cilic and was two sets to love up," de Minaur said. "I was glad I could finally get the win."
- Barty, Pliskova advance -
Reigning French Open champion Ashleigh Barty, the second seed from Australia, and Czech third seed Karolina Pliskova, chasing her first Grand Slam title, also advanced to the last 16.
Pliskova, the 2016 US Open runner-up, outlasted Tunisia's Ons Jabeur 6-1, 4-6, 6-4 while Barty dispatched Greek 30th seed Maria Sakkari 7-5, 6-3.
"Physically it was quite a tough battle," Pliskova said. "It was important to win so it doesn't matter how I feel. So pleased to be through."
Barty and Pliskova are battling top-ranked defending champion Naomi Osaka of Japan to be world number one at the end of the Flushing Meadows fortnight.
Barty has the inside track because Osaka has so many points to defend. Osaka must win the title to have any chance at staying on top while Pliskova must reach at least the semi-finals.
Former world number one Serena Williams resumes her quest for a 24th career Grand Slam title to equal Margaret Court's all-time record when she meets 44th-ranked Czech Karolina Muchova in a third round matchup at Arthur Ashe Stadium.
The 37-year-old American, six times a US Open champion, has been a runner-up in three of the past five Slams, falling to Osaka in last year's US Open final. She last won a Slam crown at the 2017 Australian Open while pregnant and hasn't won the US Open title since 2014.
Top-ranked defending champion Novak Djokovic, who has won four of the past five Slam titles and 16 overall, was set to play 111th-ranked American Denis Kudla, who has never beaten a top-10 rival in 10 tries.
The 32-year-old Serbian, a three-time US Open winner, has been no worse than a US Open semi-finalist since a third-round exit in 2006.