Djokovic blitzed Brazilian Rogerio Dutra Silva 6-2 6-1 6-2 on sun-drenched Arthur Ashe Stadium court, while Stosur used the same venue to send off American Vavara Lepchenko 7-6 6-2.
But it was Robson's gritty 6-4 6-7 6-2 triumph over former French Open champion Li, who triumphed in Cincinnati earlier this month, that created the biggest buzz at the year's final grand slam.
Robson sent four-times grand slam champion Kim Clijsters into retirement in the second round but her upset of ninth-seeded Li surely made believers of those who thought she might be a one-hit wonder.
Next up in the fourth round is Australian Stosur.
"I have had a fairly tough draw, haven't I?" the soft-spoken 18-year-old told reporters with a laugh.
"You have to beat who is in front of you. ... That's what I managed to do so far. I play Stosur now, who is defending champ. That's going to be really tough.
At 2-2 in the third set, Robson thought she had broken serve but umpire Louise Engzell ruled that the point should be replayed, even though Li had missed with her return.
The 89th-ranked Robson, however, refused to bend, breaking Li's serve twice to lead 5-2 before serving out the match.
"I wouldn't say I wasn't distracted. I was a little bit annoyed," Robson said of the umpire's call. "But that's what happens from time to time, so you've got to deal with it."
LOVE AFFAIR
While Robson's star is rising, Andy Roddick's is on the way out as the American faces up and coming Australian Bernard Tomic under the lights later Friday at Ashe Stadium in what could be his last career match.
New Yorkers have always loved Roddick and the 24,000 in attendance will surely bring that love affair to a new level given Roddick's announcement on Thursday that he is retiring after the tournament.
After the Roddick match, top seed Victoria Azarenka of Belarus takes on China's Zheng Jie, the 28th seed.
In other matches, third seeded Russian Maria Sharapova, the 2006 U.S. Open winner, advanced easily, as did Spain's fourth seed David Ferrer on the men's side.
Djokovic dropped just two games in his opening-round win over Italy's Paolo Lorenzi and Silva managed only three more as the second-seeded Serb was in a different class.
"I didn't know much about my opponent," said Djokovic. "Never saw him play. So that could have been difficult at the start in order to figure out what his game plan is. But I played well from the start to the end."
Stosur was broken in the opening game of her match, setting the tone for a gruelling first set, which lasted 59 minutes. But the Australian secured the tiebreaker 7-5 and blew through the second set over a frustrated Lepchenko in 29 minutes.
"As the match went on I probably became a little bit more comfortable, got used to her spin, and maybe the wind a little bit more," said Stosur, who lost only five games in her first two matches. "Once I got that first set then maybe I relaxed a little bit more."
