The Pole made her first grand slam final at Wimbledon earlier this summer, losing in three sets to Serena Williams, and she was never troubled in a 6-1 6-1 victory on Arthur Ashe Stadium.
Former world number one Ana Ivanovic, seeded 12th, is also through, the Serbian beating Ukrainian qualifier Elina Svitolina 6-3 6-2 in round one.
It was the end of the road, though, for 41-year-old Kimiko Date-Krumm from Japan, who continues to put aside talk of retirement but lost out 6-4 6-2 to Sweden's Sofia Arvidsson.
Radwanska retired during her first match in New Haven last week because of a right shoulder problem and wore heavy strapping on Tuesday.
The 23-year-old said: "I'm just very happy that I could give it my best in the first match. My shoulder feels better right now.
"It's always difficult. Every week it's a different surface, different balls."
Ivanovic has not played since Montreal three weeks ago because of a foot problem, and she could not have taken a break on a worse note after losing 6-0 6-0 to Roberta Vinci.
The Serb said: "In that first game I was like, 'Oh, my God at least I should win a game first'.
"In all seriousness, it wasn't easy, especially as it was one of my first matches on hard courts as well.
"It's a lot different. We have been playing on grass for a long time this season. Taking all into consideration, I'm really happy with today's performance."
Two seeds were sent packing, with 24th seed Klara Zakopalova losing 6-4 6-4 to fellow Czech Andrea Hlavackova while Russia's Elena Vesnina knocked out 32nd seed Peng Shuai from China 7-6 (7/5) 6-1.
Watch: Venus beats out Mattek-Sands... More Videos
Venus Williams has not been a factor at a grand slam for a long time but the American comes into this tournament in good form and wasted little time defeating countrywoman Bethanie Mattek-Sands 6-3 6-1 on Arthur Ashe.
It was at the US Open last year that Williams revealed she was suffering from the auto-immune disease Sjogren's Syndrome and she was a shadow of her former self in losing to Elena Vesnina in the first round at Wimbledon in June.
But the 32-year-old showed promising signs at the Olympics, where she won a fourth gold medal in the doubles with sister Serena, while she reached the semi-finals in Cincinnati two weeks ago.
Sixth seed Angelique Kerber has not looked back since a surprise run to the semi-finals here last year and she brushed aside Britain's Anne Keothavong 6-2 6-0, while there were also wins for Roberta Vinci, Dominika Cibulkova and Jelena Jankovic.
Johanna Konta continued her brilliant run at the US Open with her first ever win in the main draw of a grand slam over Hungary's Timea Babos.
The British number five's only previous experience of grand slam tennis came in the first round of Wimbledon this year when, as a wild card, she pushed top-30 player Christina McHale all the way.
Konta marked her first time in qualifying by winning three matches against higher-ranked players last week and today [Wednesday] she produced the best performance of the lot to defeat world number 59 Babos 6-2 7-5.
Laura Robson will take on Kim Clijsters in the second round of the US Open after coming through a tight tussle Samantha Crawford at Flushing Meadows.
The 18-year-old was not at her best but won the points that mattered in a 6-3 7-6 (8/6) victory - with a clash with three-time champion Clijsters, who is playing in her final professional tournament, her reward.
Robson was playing in a grand slam as a direct entrant on ranking for the first time and found herself in the unusual position of being the senior player.
American Crawford, 17, came through qualifying and is ranked only 393rd compared to Robson's 89, so this was a great opportunity for the British No.3 to reach the second round for the second successive year.
Heather Watson's US Open campaign came to an end on the first afternoon at Flushing Meadows as she was beaten 6-2 6-3 by ninth seed Li Na.
It was a very tough draw for Watson. Li has had an up and down time since winning the French Open last summer but she has well and truly hit form on the north American hard courts.
The 30-year-old reached the final in Montreal earlier this month, losing to Petra Kvitova, and then beat Agnieszka Radwanska, Venus Williams and Angelique Kerber back to back to win her first title of the year in Cincinnati.
Watson, meanwhile, was fresh from winning her second WTA Tour doubles title of the year in Texas with New Zealand's Marina Erakovic on Friday but had not won a singles match since the Olympics.