Brit Robson defied the odds to beat the Belgian 7-6 7-6 at Flushing Meadows.
The match marked Clijsters's last as a professional tennis player on the singles circuit and with that in mind, Robson took the time to pay tribute to "a great role model".
"She has been such a great player for so many years," Robson told Sky Sports News. "She's such a great role model for all the young girls. It's been great to be on the Tour with her."
Clijsters will still compete in the women's doubles and mixed doubles in New York.