Fourth-seeded Sara Errani was trounced 6-3, 6-1 by Italian compatriot Flavia Pennetta and afterward, tearfully acknowledged she was struggling to deal with the pressure and expectation of her high ranking.
Victoria Azarenka, Caroline Wozniacki, Petra Kvitova, Angelique Kerber, Jelena Jankovic and Roberta Vinci were the other top 10 seeds to win through.
Nadal improved to 17-0 on hard courts this year and the authority of his victory was enough to establish him as the favorite to win the event, let alone the looming clash with Federer.
The Spaniard saved the only break point against him in the second game of the second set, held that game and then won the next 11 to take the match in a whirlwind 95 minutes.
"In Montreal, Cincinnati, I was able to serve well, to lose very few serves," he said about the tune-up events he won before heading to New York. "So, important thing is try to find a regular serve that gives me the confidence and that gives me the possibility to start a lot of points with an advantage."
Next up for Nadal is a third-round match against Ivan Dodig, who won their only previous match on hard court, pulling out back-to-back tiebreakers in 2011 in Montreal.
"He's a very aggressive opponent, good serve, very good backhand, he goes to the net," Nadal said. "He's a tough one. I need to be playing my best if I want to have chances against him."
Federer needed only three minutes longer than Nadal to book his place in the third round, making short work of Berlocq and providing further evidence his slide to No.7 in the seedings and patchy post-Wimbledon form may have been more of a blip than a trend.
"It's one of those matches I expect myself to win if possible in straight sets and gain confidence in the process," Federer said. "All those things happened, so I'm pleased about it."
Williams, seeking her 17th Grand Slam title, brushed off an ungainly slide onto her backside en route to a typically easy second-round victory.
Second-seeded Azarenka had no trouble in defeating Aleksandra Wozniak of Canada 6-3, 6-1 and sixth-seeded Wozniacki opened the night session with a 6-1, 6-2 win over Chanelle Scheepers
Errani imploded against Pennetta. Then, while tears welled up in her eyes, Errani conceded that she's struggling to handle high expectations.
"My problem isn't that I lost," Errani said. "My problem is trying to find the desire to fight and be on the court ready to fight. For a few weeks, I haven't felt like I wanted to be on the court. That's the problem."
Errani is 5-foot-4 with energy to spare, but with loopy, unthreatening groundstrokes and a non-threatening serve. It has been, even by her account, heart and grit that helped her get to the 2012 French Open final, then follow that with a trip to the U.S. Open semifinal.
Those results, plus a tournament win and three second-place finishes on tour this year, made her the highest-seeded Italian woman ever in a major for this trip to Flushing Meadows.
But after a 6-0, 6-0 victory over a 152nd-ranked "lucky loser" in the opening round, Errani previewed what was to come, saying then that her tension was "through the roof" knowing that "everyone expects me to win 6-0, 6-0, or thinks that I can only lose against three other women in this tournament."
Then, after the loss to Pennetta, Errani tearfully acknowledged she couldn't handle the strain.
"For a couple of weeks now, I haven't been well," she said. "There's too much pressure."
