NEW YORK - Federer rolled into the fourth round with a 6-2, 6-2, 6-1 victory over Dan Evans of Britain on Friday, looking more like the guy who has won five US Open championships than the one who had dropped the opening set in his first two matches.

“At the end of the day, I think what matters the most for me is that I am in the third round, after all, after those two sort of slow starts,” Federer said. “Give myself another opportunity to do better, and I did.”

Much, much better. Federer hit 48 winners to Evans’ seven and had a 10-0 advantage in aces while winning the match in just 1 hour, 20 minutes. Defending champion Novak Djokovic’s left shoulder appeared to be just fine as he put together a straightforward, straight-set victory over Denis Kudla to reach the fourth round for the 12th appearance in a row.

The top-seeded Djokovic won 6-3, 6-4, 6-2 under the lights in Arthur Ashe Stadium. He had complained about pain in his shoulder and repeatedly was visited by a trainer during his previous match. Serena Williams, who had also dropped the first set in her previous match, moved to the fourth round by beating Karolina Muchova 6-3, 6-2.

Federer had dropped the opening set in his first two matches for the first time in his 19 US Open appearances. No man has done that and gone on to win the tournament, but the No. 3 seed isn’t one to worry about history. Nor is he superstitious, which is why he didn’t care when asked if it was OK if his family and support staff moved from their usual spot in the stadium to another, where they could find more shade. Supporters of Evans were on the sunny side.

Federer agreed that it was a disadvantage for Evans to play two days in a row while he had an extra day off, but grew angry when asked if he had lobbied to play early. Evans, while praising Federer’s performance, was disappointed in his schedule after playing four sets Thursday to upset No. 25 Lucas Pouille.  The night match should benefit Djokovic, who was bothered a left shoulder injury that required treatment during his second-round match. The defending champion hoped to be feeling better by the time he faced Denis Kudla on Friday night.

And he hoped to avoid the upsets that knocked out another contender when No. 7 Kei Nishikori lost 6-2, 6-4, 2-6, 6-3 to Alex de Minaur. There were already more unseeded players (17) than seeded players (15) left going into the third round, the first that had happened at the US Open since the tournament was expanded to 32 seeds in 2001.

The women’s field nearly lost one of its top seeds, but 2016 runner-up Karolina Pliskova held on to edge Ons Jabeur 6-1, 4-6, 6-4 and reach the fourth round. No. 2 Ash Barty had an easier time, beating No. 30 Maria Sakkari 7-5, 6-3.