Clijsters, whose Grand Slam title haul also includes last year's Australian Open, had not lost at the US Open since falling to compatriot Justine Henin in the 2003 final on the same Arthur Ashe Stadium court.
"This feels like the perfect place to retire. I just wish it wasn't today," Clijsters said. "I gave it all and just wasn't good enough at the end of the match."
Robson snapped the Belgian's 22-match US Open win streak, smacking a tricky forehand winner on the line on the penultimate point and firing a service winner to claim the victory on her third match-point chance.
"I was just trying to play as hard as I could because I knew if I didn't Kim would dominate because she's such an aggressive player," Robson said. "I just went out there to keep getting the ball back and work my butt off."
Robson, who was age five when Clijsters first played here, will next face Chinese ninth seed Li Na, who dispatched Australia's Casey Dellacqua 6-4, 6-4, in 87 minutes.
"Thanks to Kim for being such a great role model to me for so many years," Robson said. "It was a great pleasure to finally get to play against you."
Clijsters, 29, made her final bow on the same court where she won her first Grand Slam title in 2005 and followed it up with crowns in 2009 and 2010. She had said she was leaving the sport for more time as a wife and mother.
"One of my biggest dreams came true in 2005 winning here," Clijsters said. "Every time I came back I was so inspired by the enegry that was out on this court and I played some of my best matches on this court.
"It has all been worth it. But I look forward to having the next part of my life coming up."
British third seed Andy Murray reached the third round with a 6-2, 6-1, 6-3 win over Ivan Dodig of Croatia.
Murray will face either 30th seed Feliciano Lopez or Pablo Andujar, both Spanish, for a place in the last 16.
World No. 1 Victoria Azarenka, this year's Australian Open champion, reached the third round while defending champion Samantha Stosur and third seed Maria Sharapova, the reigning French Open champion, advanced with ease as well.
Spanish fourth seed David Ferrer, Argentine seventh seed Juan Martin Del Potro and US ninth seed John Isner won their openers on the Flushing Meadows hardcourts.
The US Open has seen nine men's comeback triumphs from two sets down in the first round, matching the record from 1989, including Serbian ninth seed Janko Tipsarevic's 4-6, 3-6, 6-2, 6-3, 6-2 victory over Frenchman Guillaume Rufin.
And Australian Lleyton Hewitt, the 2001 US Open champion, reached the second round by dispatching Germany's Tobias Kamke 4-6, 6-2, 6-1, 6-4.
Reigning Australian Open champion Azarenka reached the third round by defeating Belgian qualifier Kirsten Flipkens 6-2, 6-2 in only 65 minutes for her 50th match victory of the season.
"I'm proud of everything I have achieved this season," she said. "It has been a great year."
The 23-year-old from Belarus, whose 26-match win streak to begin the season was the best women's start since 1997, seeks her 13th career title and fifth trophy of the year on the Flushing Meadows hardcourts.
"I would love to play for the title," Azarenka said. "It's a long way."
Azarenka, who has reached the last eight in every Grand Slam event except the US Open, will next face Chinese 28th seed Zheng Jie, who beat Slovakian qualifier Magdalena Rybarikova 6-3, 6-1.
Australian seventh seed Stosur took an hour to beat Romanian qualifier Edina Gallovits-Hall 6-3, 6-0 to reach a third-round date with US 31st seed Varvara Lepchenko.
Russian third seed Sharapova ripped Spain's Lourdes Dominguez Lino 6-0, 6-1 to book a third-round match against 21-year-old US wildcard Mallory Burdette, ranked 252nd, who advanced with a 6-2, 6-4 victory over Czech Lucie Hradecka.
Ferrer, who became the top seed in his quarter of the draw when compatriot Rafael Nadal pulled out with knee problems, defeated South Africa's Kevin Anderson 6-4, 6-2, 7-6 (7/3).
"I'm happy. I played good. I tried to play solid and consistent," Ferrer said.
Ferrer, whose best Grand Slam showing was a 2007 US Open semi-final run, booked a second-round match against Dutch qualifier Igor Sijsling, who beat Spain's Daniel Gimeno-Traver 7-5, 6-3, 6-4.
Isner, the top American hope to end a nine-year US men's Grand Slam title drought, struggled to subdue Xavier Malisse 6-3, 7-6 (7/5), 5-7, 7-6 (11/9).
"I had my hands full," Isner said. "It got to the point where it was anyone's match and I'm pretty fortunate to move on."
Del Potro, the 2009 US Open winner, advanced over France's Florent Serra 6-4, 7-6 (7/4), 6-4.
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