Li, seeded fifth after reaching the Australian Open final earlier this season, needed 81 minutes to avenge her third round loss to Robson at Flushing Meadows last year.
"At least this year I'm in the second week," said Li, whose next opponent will be either Serbia's Jelena Jankovic or Japan's Kurumi Nara.
As a former French Open champion and two-time Australian Open finalist, Li had too much experience and firepower for the British teenager, 12 years her junior.
The 31-year-old Li was rewarded for her aggressive approach, hitting 23 winners and banging down 11 aces on a windy day at Arthur Ashe Stadium.
"I was a little bit surprised because today I have a lot of aces. It was like, wow." Li said.
Robson contributed to her own downfall by committing 30 unforced errors, 15 in each set, but was satisfied with her overall performance in the tournament.
"I'm disappointed about today for sure and I thought I could have played a lot better," she said. "But I always knew it was going to be a tough match. All in all, I guess it was an average week.
"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 over the last 12 months."
Still just 19, Robson is making steady improvement each season and was the first British woman to be seeded at a Grand Slam in more than a quarter of a century.
"I think I'm going in the right direction. I feel like I'm improving and working on a more all-around game," she said.
"It's going to take a lot of hard work, but I'm willing to do that."