The Swiss great was brimming with confidence from the start, taking advantage of the speedy hardcourts under the open roof at Arthur Ashe Stadium on a warm and sunny day.
Federer, who is seeking his sixth US Open title, rifled 48 winners and 10 aces to see off the overmatched Evans, who is now 0-3 lifetime against the 38-year-old.
Federer has had limited court time since his epic defeat to Novak Djokovic at the Wimbledon final in July but appeared to shake off any remaining rust with the win.
“I really enjoyed myself today. Beautiful sky and you guys out here also helped,” he said in an on-court interview in front of an adoring crowd.
Next up for third seeded Federer is a meeting with either Pablo Carreno Busta or David Goffin, and Federer said he would not underestimate either opponent.
“They are both really quality baseliners,” he said, adding that he expected the 15th seed Goffin to come out on top in his tie with the Spaniard.
“I expect it to be tough, not like today anyway.”
Meanwhile, Australia’s Alex de Minaur knocked out 2014 US Open finalist Kei Nishikori the third round to collect his first victory over a top-10 player.
The 20-year-old Aussie, ranked 38th, advanced 6-2, 6-4, 2-6, 6-3 in just under three hours. De Minaur will face Bulgaria’s Grigor Dimitrov or Polish lucky loser Kamil Majchrzak in the last 16.
In women’s action, Czech third seed Karolina Pliskova, chasing her first Grand Slam title, advanced to the fourth round by outlasting Tunisia’s Ons Jabeur 6-1, 4-6, 6-4.
Pliskova, the 2016 US Open runner-up who could finish the fortnight as world number one, booked a spot in the last 16 against either British 16th seed Johanna Konta or China’s 33rd-seeded Zhang Shuai.
After taking the first set in 26 minutes, Pliskova broke to open the second. Jabeur, ranked 62nd, had her right knee retaped and battled back to break Pliskova three times in the second set, the last on a forehand winner to force a third set.
Pliskova broke to start the third set and seized another in the fifth game on an errant Jabeur forehand before advancing on a backhand winner after two hours and eight minutes.
“She improved the game a lot in the second set, she hit a couple unbelievable shots and got into her rhythm,” Pliskova said.
“Especially had to serve well. Was able to hit a couple aces in the third set which really helped. Physically it was quite a tough battle. It was important to win so it doesn’t matter how I feel. So pleased to be through.”
Pliskova, 27, is battling top-ranked defending champion Naomi Osaka of Japan and Australia’s second-ranked Ashleigh Barty, the French Open winner, for the world number one spot.
Barty, who faces Greek 30th seed Maria Sakkari later, 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.
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