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Radwanska, promoted to third seed after the injury-forced withdrawal of Maria Sharapova, defeated Spanish world number 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, was on course for a quick-fire win over Torro-Flor, her second successive Spanish opponent, when she raced through the first set in just 21 minutes, losing just seven points.
But Torro-Flor, dressed in matching colours of blue and pink, made the Pole work for her win in the second set with three breaks of serve.
Radwanska, however weathered the unexpected storm, going through to a third-round clash against Russia's Anastasia Pavlyuchenkova, capitalising on her rival's 38 unforced errors and 10 double faults.
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.
The Chinese star will next face either British 30th seed Laura Robson, who knocked her out of the tournament in 2012, or France's Caroline Garcia.
"Both players have improved a lot in the last year," said Li. "I look forward to the chance of playing Laura."
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 a schedule which will see even first-round matches in the mixed doubles completed before he takes the court.
Having ended Britain's embarrassing Grand Slam hoodoo with his US Open breakthrough 12 months ago, Murray starts his first major as a defending champion against Michael Llodra, the 33-year-old Frenchman who is edging towards retirement.
The 26-year-old Murray has added the Wimbledon title since winning in New York in 2012, comfortably burying for ever all talk of Fred Perry, the country's last men's champion at a major in 1936.
Meanwhile, rain halted play delaying the start of matches for past champions Venus Williams and Juan Martin del Potro.
Williams, the 60th-ranked winner of the 2000 and 2001 US Opens, was set to face China's 56th-ranked Zheng Jie at Louis Armstrong Stadium.
Argentina's fourth-seeded Del Potro, the 2009 US Open winner, was preparing to meet Spain's Guillermo Garcia-Lopez at Arthur Ashe Stadium.
US Open results on Wednesday (x denotes seeded player):
Men's singles:
First round:
Marcos Baghdatis (CYP) bt Go Soeda (JPN) 6-4, 6-3, 6-1
Women's singles:
Second round:
Carla Suarez Navarro (ESP x18) bt Coco Vandeweghe (USA) 6-3, 6-4
Agnieszka Radwanska (POL x3) bt Maria-Teresa Torro-Flor (ESP) 6-0, 7-5
Anastasia Pavlyuchenkova (RUS x32) bt Ashleigh Barty (AUS) 6-4, 6-0
Li Na (CHN x5) bt Sofia Arvidsson (SWE) 6-2, 6-2
