Radwanska, promoted to third seed after the injury-forced withdrawal of Maria Sharapova, defeated Spanish World No 103 Maria-Teresa Torro-Flor, 6-0, 7-5 while Li, the Chinese fifth seed, beat 100th-ranked Swede Sofia Arvidsson 6-2, 6-2.
Radwanska, who has never got beyond the fourth round in New York, will now face Russia’s Anastasia Pavlyuchenkova.
Li, playing in her 30th Grand Slam and a New York quarter-finalist in 2009, clinched her third career win over policeman’s daughter Arvidsson, who has now not progressed beyond the second round in seven attempts.
Meanwhile, Murray begins the defense of his title almost 48 hours after second seed Rafael Nadal, viewed as the most likely contender to triumph this year, started his campaign.
“I’m playing my first round match at the us open at 7pm on a wednesday...,” tweeted Murray in thinly-veiled frustration at the scheduling.
>> Men’s singles (Rd 1)
Marcos Baghdatis bt Go Soeda 6-4, 6-3, 6-1
>> Women’s singles (Rd 2)
Agnieszka Radwanska (3) bt Maria-Teresa Torro-Flor (ESP) 6-0, 7-5
Carla Suarez Navarro (18) bt Coco Vandeweghe 6-3, 6-4
Anastasia Pavlyuchenkova (32) bt Ashleigh Barty (AUS) 6-4, 6-0