For Federer and Williams, it was business as usual at Flushing Meadows but not for Italy's Sara Errani, the women's fourth seed.
Crumbling under the weight of expectation, Errani crashed to a 6-3 6-1 loss to compatriot Flavia Pennetta, then made the startling admission she choked under pressure.
"I don't know why, but I'm not enjoying going on the courts," she confessed. "And that is the worst thing a player can have."
Federer, unflappable even as he struggles to add to his record collection of 17 Grand Slam singles titles, hardly raised a sweat as he brushed aside Argentina's Carlos Berlocq 6-3 6-2 6-1.
"For me it was pretty straightforward, to be honest," Federer said. "It's one of those matches I expect myself to win if possible in straight sets and gain confidence in the process.
"All those things happened, so, yeah, I'm pleased about it."
Williams was also unflustered even though the wind was blowing hard when she strolled on to the Arthur Ashe Stadium centre court.
Her match against Galina Voskoboeva of Kazakhstan had originally been scheduled for Wednesday but was held over because of rain. Unfazed, she cruised to a 6-3 6-0 win.
"I'm just trying to do the best I can," Williams said. "Just always trying to get a little better."
With Wednesday's rain giving way to brilliant sunshine, most of Thursday's other daytime matches went according to the rankings with none of the men's seeds losing.
David Ferrer, the men's fourth seed and this year's French Open finalist, beat fellow Spaniard Roberto Bautista 6-3 6-7(5) 6-1 6-2.
Richard Gasquet, Janko Tipsarevic and Dmitry Tursunov all won without dropping a set. If there was surprise in the men's draw, it was when Dan Evans toppled Australia's Bernard Tomic 1-6 6-3 7-6(4) 6-3.
Evans, who is ranked 179th in the world and had to come through the qualifiers just to make the main draw, upset Japan's Kei Nishikori in the first round then followed up by beating Tomic, ranked 52nd.
Petra Kvitova, Ana Ivanovic and Jelena Jankovic were among the winners in the women's draw, which lost four seeds, the most notable being Errani.
One of the sport's rising stars, ranked number one in the world in doubles and fifth in singles, she admitted after her loss that she was overcome by pressure.
The 26-year-old, who was promoted to fourth seed when Maria Sharapova pulled out of the tournament, said she had been shaking and struggling to sleep for four days and did not want to go on court.
"I don't want to go to play. I don't want to stay there on the court. I feel very bad," she said. "So that is the problem for me."
- Sports & Recreation
- Sara Errani
- Flavia Pennetta