No problems for Ivanovic
Ana Ivanovic, seeded 13th in New York, had a comfortable win, beating Alexandra Dulgheru of Romania 6-2 6-1 at the US Open.
Ivanovic can certainly empathise with Errani having reached world number one following her French Open victory in 2008 and then wilted under the pressure.
She has spent the last five years trying to get back to the same level, and is yet to manage it.
The Serbian said: "I think it's harder to stay there than to get there because the expectations are higher. Everyone is playing their best tennis against you and trying to beat you and to bring you down.
"There is obviously pressure from your own country, from the media, and everything else that you put on yourself, the expectations that you have from yourself. And sometimes when you don't match that, if you're a perfectionist, it can actually hurt you.
"This was probably the hardest lesson that I learned. Now, looking back, I wish I just trusted myself."
Sixth seed Caroline Wozniacki played the first match of the night session on Arthur Ashe and brushed aside Chanelle Scheepers of South Africa 6-1 6-2.
The Dane is the highest seed left in the third quarter of the draw after Errani's exit and looks in good form.
There were no more late-night heroics from 17-year-old American Victoria Duval, who lost to Daniela Hantuchova 6-2 6-3.
The qualifier produced the performance of the day on Tuesday to knock out former champion Sam Stosur but was well beaten by the Slovakian.