NEW YORK — Only a few spots separate them in the seedings. Still, the considerable gulf between No. 1 Serena Williams and No. 4 Sara Errani was hard to ignore in their back-to-back matches Thursday at the US Open.
Williams, seeking her 17th Grand Slam title and second straight at Flushing Meadows, brushed off an ungainly slide onto her backside en route to a typically easy second-round victory, 6-3, 6-0 over Galina Voskoboeva in half-full Arthur Ashe Stadium.
Barely worth talking about by Williams’s standards. ‘‘I’ll have to think about it and see what I can do better, but it was OK,’’ she said.
Only an hour before on the same court, a much different scene: Errani imploded in a 6-3, 6-1 loss to her Italian teammate, 83d-ranked Flavia Pennetta. Then, with tears welling in her eyes, Errani conceded that she’s struggling to handle her high ranking and the high expectations that have come with that.
‘‘My problem isn’t that I lost. I’ve lost a million times in my life,’’ 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.’’
That concession was the most unexpected development on Day 4 of the US Open, where the tournament got back on track after a rainy Wednesday that postponed eight women’s matches and shuffled the lineups.
Among the results from Thursday’s full slate:
Rafael Nadal saved the only break point against him in a 6-2, 6-1, 6-0 rout of qualifier Rogerio Dutra Silva. He’ll head into the third round still not having lost his serve in the tournament — and still undefeated on hard courts, at 17-0, this season.
No. 4 seed David Ferrer overcame an error-filled, second-set tiebreaker to top Roberto Bautista Agut, 6-3, 6-7 (5-7), 6-1, 6-2.
Second-seeded Victoria Azarenka defeated Aleksandra Wozniak of Canada, 6-3, 6-1.
Sixth-seeded Caroline Wozniacki beat Chanelle Scheepers, 6-1, 6-2, to open the night session.
Victoria Duval, after upsetting 2011 champion Sam Stosur, ran into a veteran player 12½ years her senior who reminded everyone that the young American is still a 296th-ranked qualifier as Daniela Hantuchova won, 6-2, 6-3.
No. 13 seed John Isner, the highest-ranking American man, overcame right leg pain and support for his French opponent, 39th-ranked Gael Monfils, to reach the third round for the fifth consecutive year with a 7-5, 6-2, 4-6, 7-6 (7-4) win.
Williams got through her win unscathed, and when she was done in Ashe Stadium, five-time champion Roger Federer, the seventh seed, dispatched Carlos Berloq, 6-3, 6-2, 6-1, in 1 hour, 35 minutes.
‘‘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, yeah, I’m pleased about it.’’
American Christina McHale won a three-setter over Elina Svitolina, while another US player, 81st-ranked Allison Riske, had an easier time in a 6-4, 6-2 victory over Mona Barthel.
‘‘You never know at these things,’’ Riske said after making the third round of her second straight Grand Slam tournament. ‘‘Anything can happen. That’s kind of the beauty of tennis in general. Ranking is kind of just a number.’’
Victoria Duval, the 296th-ranked, 17-year-old American who earned her first victory in a Grand Slam tournament Tuesday, was also in action later.
Isner was the last seeded American in the men’s draw after No. 26 Sam Querrey lost in four sets to Adrian Mannarino. Another US man, 20-year-old Jack Sock, moved to the third round with a 7-6 (7-3), 1-6, 7-5, 6-2 win over Maximo Gonzalez of Argentina.
Williams was pushed only briefly against Voskoboeva, ranked 77th from Kazakhstan.
Serving at game point trailing, 5-3, Voskoboeva drew Williams to the net, and as Williams reached for the ball, her feet slid out from under her and she fell hard onto her backside, her racket slamming to the ground. Before she fell, however, she reached the shot to win the point. Two points later, she closed out the set.
The second set took all of 27 minutes. When it was over, Williams was sitting at the same table where Errani had cried earlier, being asked how she would advise the Italian, who said she was ‘‘destroyed by the pressure’’ of returning to the French Open this year, where she followed her 2012 appearance in the final with a run to the semifinals.
‘‘I really wouldn’t know what to say,’’ Williams said. ‘‘I can only say that I think she’s doing a good job. I mean, sometimes you have a tough day at the office, and it doesn’t mean that you don’t handle the pressure well.’’
But Errani said she didn't.
She is 5 feet 4½ inches, with energy to spare, but with loopy, unthreatening groundstrokes and a serve that maxes out at around 85 miles per hour. 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 US Open semifinal, where she lost, 6-1, 6-2, to Williams.
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 152d-ranked ‘‘lucky loser’’ in the opening round, Errani previewed what was to come, saying then that her tension was ‘‘through the roof.’’
Then, after the loss to Pennetta, Errani tearfully acknowledged she couldn’t handle the strain.
It didn’t help, of course, that she was playing an opponent with nothing to lose, the way many players react when they face someone in the top five. Last year, Pennetta missed the US Open and the entire end of the season while she recovered from surgery on her bad right wrist.