With a possible semi-final showdown with Federer looming, Britain's Andy Murray remained in the hunt for his first grand slam crown by defeating Spain's Feliciano Lopez to reach the fourth round.
Women's second seed Agnieszka Radwanska of Poland set up a fourth-round tussle with Italy's Roberta Vinci by easing by former world number one Jelena Jankovic 6-3 7-5 at a steamy Arthur Ashe Stadium.
"With the hot conditions you really have to fight yourself more than your opponent," said Radwanska, a sentiment echoed by several players.
Federer cruised past Fernando Verdasco 6-3 6-4 6-4 in two hours and two minutes, blasting seven aces and 30 winners against the 25th-seeded Spaniard.
The five-time US Open champion, who has not dropped a set in the tournament, next faces American Mardy Fish or Frenchman Gilles Simon for a place in the quarter-finals.
Verdasco, 28, had 35 unforced errors and 10 double faults as he lost to Swiss Federer for the fifth time in as many meetings.
Williams, seeking her fourth US Open title, needed a break of serve in the final game of the opening set to grab the momentum as she ousted Russian Ekaterina Makarova 6-4 6-0.
Makarova buckled under the pressure of her first-set letdown and was blown away in the second in just 32 minutes.
The Russian knocked out Williams in the fourth round of this year's Australian Open and the American said she was "motivated" to turn the tables at the year's final grand slam tournament.
The 30-year-old Williams, a 14-time grand slam champion, said it was painful to watch a video of her defeat by Makarova.
"Knowing that I lost (I thought it) could definitely happen again," said the Wimbledon and London Olympic champion. "I did not want that to happen.
"Whether I learned something from that match, I don't know. I really hate watching matches that I lose unless I'm punishing myself."
Williams punished Makarova on Saturday, enjoying a 31-10 advantage in winners and claiming all eight of her service games.
Murray, who also won Olympic gold last month, recovered from a mid-match lapse to defeat Lopez 7-6 7-6 4-6 7-6 in three hours and 53 minutes.
The Briton was leading 4-2 in the third set before Lopez fought back to send the match into a tense fourth set.
Third seed Murray next plays American wildcard James Blake or 15th-seeded Canadian Milos Raonic.
"It was challenging on both fronts, mentally and physically," said the Scot.
"I usually have three weeks in Miami before the US Open but I couldn't this year because of the Olympics. It was a nice problem to have though."
