On a breezy day in Queens, it was Li who settled quicker, establishing an early rhythm from the back of the court as she raced into a 3-0 lead. By the time Robson began to find her range the set was beyond her, Li wrapping it up in just 29 minutes.
However, after barely coughing up an error in this first half hour on court, Li allowed Robson back into it with a couple of lapses on serve at the start of the second.
Since teaming up with Carlos Rodriguez 12 months ago, Li has cut a calmer and more focused figure on court, and she responded well to this setback, cutting down the errors and earning the break back when Robson could only push a forehand long after another punishing rally.
A few games later, she broke again before calling on another Rodriguez project, the serve, to get her over the finish line, wrong-footing Robson on match point with a second serve ace.
"First, I just want to say thanks to the crowd for supporting me," Li said to Rennae Stubbs during her on-court interview. "I was really pleased with how I was hitting it and I was also serving well."
Despite failing to replicate her performance from 12 months ago, Robson was keen to accentuate the positives of her second visit to New York. "I'm disappointed about today, for sure, but I feel I'm a more confident player than last year," she said. "In my first two rounds I thought I played really well and I closed out the matches really well, which is something that has improved a lot recently. I think I'm going in the right direction."
In addition to her excellence from the back, Li once again showed a greater willingness to come to the net, although she admitted she was not expecting much in the way of praise from her coach. "In public, maybe Carlos will say I am doing well at the net, but in private he will tell me I could come in even more!"
Should Li win her fourth round, against either Jelena Jankovic or Kurumi Nara, she is seeded to meet No.3 seed Agnieszka Radwanska, who withstood a baseline barrage from Anastasia Pavlyuchenkova to keep her title challenge on course with a 64 76(1) victory.
"I'm very happy that I won another match in two sets," Radwanska said. "Of course it was two tight sets and actually it was just by a couple points in each one.
"But definitely I played a very high level in the tie-break. I was really focused from the beginning, and I just wanted to win it very much."
Pavlyuchenkova trains at the Mouratoglou Academy in Paris, and Radwanska sees some similarities with one of its other attendees, Martina Hingis. "I think we have a similar style," Radwanska added. "We don't have powerful games or hit big bombs like some of the others.
"We are more about mixing everything up and always trying to find a way to win the point, just not all the time with power."