The defeat of Belgian Clijsters grabbed the attention as the first significant upset of the tournament.
Clijsters, three-times a U.S. Open champion, remains in the doubles and mixed doubles but the loss to Robson was her final singles match before she quits the tour to concentrate on family life.
She saved two match points in the 12th game of the second set with a searing forehand volley and a huge first serve.
The tiebreak was tense as Clijsters fought to extend her career but Robson, the world number 89 playing with fearless aggression and pinpoint accuracy, converted her third match point and it was all over for the 29 year old.
"I have played some of my best tennis here and some of my best matches," Clijsters said.
"It is a place that has inspired me. This feels like the perfect place to retire - but I just wish it wasn't today.
"I fought and gave it my all but just wasn't good enough in the end.
"It's been a great adventure. It's all been worth it but I'm looking forward to the next part of my life."
Robson paid tribute to Clijsters in an on-court interview.
"I was just trying to play as well as I could because if I didn't, I knew Kim would completely dominate," Robson said.
"I want to say thanks to Kim for being such a great role model for so many years. I have grown up watching you play and it has been an honour to finally play against you."
Other matches on Wednesday went mostly to script, the only mild surprises involving lower seeds.
World number one Victoria Azarenka overpowered Belgian qualifier Kirsten Flipkens 6-2 6-2 in 65 minutes in a blustery Arthur Ashe Stadium before defending champion Sam Stosur recorded a routine 6-3 6-0 win over Edina Gallovits-Hall.
Stosur met Redfoo of the music group LMFAO before he watched her match and his presence at courtside inspired a victory dance by the Australian.
"I figured, well, there's only going to be maybe one chance you can do that at the U.S. Open with him there," Stosur said. "I'm sure I looked like a goose."
Russia's third seed Maria Sharapova trounced Lourdes Dominguez Lino 6-0 6-1 in the first of two night matches.
Murray was equally untroubled in his win over Dodig and thousand of spectators walked out before the match was completed.
Scratchy in his opening round match against Alex Bogomolov, the Scot had all guns blazing against Dodig.
Elsewhere in the men's draw, fourth-seeded David Ferrer disposed of Kevin Anderson 6-4 6-2 7-6 and local hope John Isner won a high-quality clash with Xavier Malisse 6-3 7-6 5-7 7-6.
"A lot of people are projecting me to go far here but I wasn't looking past this match," the ninth-seeded Isner said.
"As you guys could see, I had my hands full. Got to a certain point there where it was anyone's match."
Ernests Gulbis defeated 21st seed Tommy Haas 3-6 4-6 6-4 7-5 6-3 and Gilles Muller snuck home for a 2-6 3-6 7-5 7-6 7-6 defeat of 28th seed Mikhail Youzhny to join Tipsarevic in the band of players who have come back from the brink.
"I had to grind and suffer and do whatever was necessary to win," Tipsarevic said.
Former men's champion Juan Martin del Potro as well as top women Petra Kvitova and Li Na all progressed with routine victories.
Flandersnews and Reuter