Wozniacki, who captured a fourth straight New Haven title this past weekend, leads the WTA with six championships this season, but failed to get past the fourth round at the last two Grand Slam events -- the French Open and Wimbledon.
The 21-year-old Dane, who is currently dating U.S. Open golf champion Rory McIlroy, is still seeking her first-ever major title.
When asked if she was playing well enough to capture the U.S. Open, Wozniacki said: "Well, always first match is tough to indicate anything. But, you know, happy to be through. I definitely still have a chance because now there's only 64 left."
"I've won a lot of tournaments. I'm No. 1 in the world, and of course I can still improve," the happy-go-lucky Dane added.
Wozniacki will face Dutchwoman Arantxa Rus in the second round.
The Belarusian Azarenka, meanwhile, handled overmatched Swede Johanna Larsson 6-1, 6-3 in 70 minutes at Ashe.
"There are always things that could have been done better, but I think I had a pretty solid start," Azarenka said. "I kept control of the match, so it's important, you know, to have that control in the opening rounds."
The 22-year-old Azarenka reached her first career Grand Slam semifinal last month at Wimbledon. The U.S. Open is the only major event where she has failed to reach a quarterfinal.
Sixth-seeded Li Na suffered the biggest upset of the day, as Romanian teenager Simona Halep took out the French Open champion and Aussie Open runner-up from China in 6-2, 7-5 fashion. The promising Halep is a 19-year-old who is ranked 53rd in the world.
Li's loss leaves the U.S. Open without a Grand Slam champion from this season. Aussie Open champ Kim Clijsters was unable to play here, while Wimbledon winner Petra Kvitova lost on Monday, and Li exited the draw on Tuesday. This particular U.S. Open scenario hasn't happened since 1971.
Seventh-seeded Italian grinder Francesca Schiavone barely moved on with a hard-fought 6-3, 1-6, 6-4 victory over Kazakhstan's Galina Voskoboeva. Schiavone committed four double-faults while trying to serve out the match, but then broke Voskoboeva's serve to seal the win.
"Not good serve," Schiavone said. "Can't happen, better it happen now than maybe to be longer, three, four games, but it was just two games bad, really bad."
Schiavone advanced despite piling up 16 double faults on Day 2. The 31-year- old was this year's French Open runner-up and last year's surprise titlist at Roland Garros.
Tenth-seeded rising German Andrea Petkovic pasted Russian Ekaterina Bychkova 6-2, 6-2, while former world No. 1 Jelena Jankovic eased her way past American Alison Riske 6-2, 6-0. Petkovic was a quarterfinalist at this year's Aussie and French Opens. The 11th-seeded Serbian Jankovic was the U.S. Open runner-up three years ago.
Russian Svetlana Kuznetsova, who is seeded 15th and was the 2004 champion and 2007 runner-up in Flushing, downed Italy's Sara Errani, 7-5, 6-1.
Another former No. 1 from Serbia, 16th-seeded Ana Ivanovic, got past Russian Ksenia Pervak 6-4, 6-2. Ivanovic is a former French Open champion and Aussie Open runner-up.
Anastasia Pavlyuchenkova, the 17th seed from Russia, defeated Anna Tatishvili, 6-2, 6-2.
Meanwhile, 22nd-seeded German Sabine Lisicki stayed hot by leveling Ukrainian Alona Bondarenko 6-3, 6-3 and 26th-seeded Italian Flavia Pennetta pasted France's Aravane Rezai 6-1, 6-4 on the grounds at the USTA Billie Jean King National Tennis Center. The rising Lisicki was last week's hardcourt titlist in Dallas, where she beat Rezai in the final, and reached her first career major semi at the All England Club last month.
Lisicki's second-round opponent will be unseeded Venus Williams, the former world No. 1 who is a seven-time Grand Slam champ, including U.S. Open titles back in 2000 and 2001.
"We played twice, and twice we had a very, very good match," Lisicki said about her upcoming bout with Venus." So, you know, I think it really depends who plays better that given day and that person will win, I think."
Eighteenth-seeded Italian Roberta Vinci vaulted past Romanian Irina-Camelia Begu 6-3, 6-4; 20th-seeded Belgian Yanina Wickmayer handled Romanian Sorana Cirstea 6-1, 7-5; 21st-seeded Slovakian Daniela Hantuchova was beaten by France's Pauline Parmentier, 6-2, 6-3; 23rd-seeded Israeli Shahar Peer outlasted Indian Sania Mirza 6-7 (5-7), 6-3, 6-1; 29th-seeded Australian Jarmila Gajdosova got past Czech Iveta Benesova, 7-6 (7-5), 7-5; 31st-seeded Estonian Kaia Kanepi topped Thai veteran Tamarine Tanasugarn 6-4, 6-3; and No. 32 seed Maria Jose Martinez Sanchez of Spain was taken down by Germany's Mona Barthel, 6-3, 6-4.
Several other women reached the second round, including former top-10 performer Jelena Dokic and American teenager Coco Vandeweghe, who dismissed Italian Alberta Brianti 7-5, 6-3. Dokic will battle Jankovic in her next outing. The 19-year-old Vandeweghe is the niece of former NBA player, coach and general manager Kiki Vandeweghe.
Up next for Vandeweghe will be ninth-seeded former French Open runner-up Samantha Stosur of Australia.
Another first-round win came for Argentine veteran Gisela Dulko, who should have her hands full with Azarenka in the round of 64.