Radwanska, who has never got beyond the fourth round, next plays Russia’s Anastasia Pavlyuchenkova.
Li, playing in her 30th Grand Slam and a New York quarter-finalist in 2009, will next face 30th seed Laura Robson in a rematch of their clash 12 months ago, which the British player won.
Robson defeated France’s Caroline Garcia 6-4, 7-6 (7/5) to book her third-round slot.
Among men’s seeds heading for the exit were Italian 16th seed Fabio Fognini, who lost 6-1, 6-2, 6-2 to Rajeev Ram of the US.
Jurgen Melzer, the 29th-seeded Austrian, who captured the Winston-Salem title at the weekend, slumped 7-5, 6-3, 7-6 (7/3) to Russia’s Evgeny Donskoy, while Alex Bogomolov of Russia sent French 24th seed Benoit Paire packing with a 7-5, 2-6, 6-4, 5-7, 7-6 (7/5) win.
Croatian qualifier Ivo Karlovic placed American James Blake into retirement with a 6-7 (2/7), 3-6, 6-4, 7-6 (7/2), 7-6 (7/2) win.