Errani, last year's French Open runner-up, was in tears after falling to 83rd-ranked Flavia Pennetta 6-3 6-1 in 71 minutes.
"It was difficult,'' Errani said. ``The worst thing was the `fight.' Normally it's the best thing I do on the court and today it was not good. I don't know why. I think it's the pressure. Everything was very difficult for me.''
Pennetta, a former world number 10, said the hardest part for her was facing a friend.
"We know each other really well,'' she said. ``It's not easy to play against your friend so well but you have to get on the court and play your best.''
Pennetta improved to 4-2 against Errani in their first meeting off clay, smacking seven aces and 33 winners.
Pennetta will next face Russian 29th seed Svetlana Kuznetsova, the 2004 US Open winner who defeated China's 37th-ranked Peng Shuai 6-1 4-6 6-4.
"I never beat her. She's a really good player, a strong powerful player,'' Pennetta said. "She also doesn't have a lot of good wins the last two years and she is also my friend, but you have to put that aside when you go on the court.''
In another upset, Japanese qualifier Kurumi Nara advanced to the third round by defeating Romanian 19th seed Sorana Cirstea 7-5 6-1. Nara next faces Serbian ninth seed Jelena Jankovic, who beat Russian Alisa Kleybanova 6-3 6-2.
On the men's side, Russian 32nd seed Dmitry Tursunov advanced 7-6 (7-4) 1-1 when Frenchman Guillaume Rufin retired.
Spanish second seed Nadal, unbeaten on the hardcourts this year to become one of the favorites to claim the crown, will make his bid for a place in the third round in a night match against Brazilian qualifier Rogerio Dutra Silva.
Swiss 17-time Grand Slam champion Federer, at his lowest seed in Flushing Meadows since 2002 at seventh, will meet Argentina's 48th-ranked Carlos Berlocq as he tries to reach the third round, something he could not do at Wimbledon.
Federer lost for the first time in 50 tries in a Grand Slam second-round match last month at Wimbledon, falling to 116th-rated Sergiy Stakhovsky in his earliest Slam exit since the 2003 French Open.
-AAP