The 22-year-old Serb beauty has been mired in a rut since winning the French Open in 2008 and taking the world number one spot.
She failed to cope with the sudden celebrity and status and saw her world ranking plummet throughout 2009.
But after taking on Steffi Graf's former coach, Heinz Gunthardt, as her mentor in February this year, Ivanovic has been gradually working her way back.
Unseeded for New York, she swept past Zheng, the 23rd seed, who reached the Australian Open semi-finals in January, in just 56 minutes on the Arthur Ashe Centre Court.
Ivanovic next goes up against French wildcard Virginie Razzano of France who ousted 13th seeded compatriot Marion Bartoli 7-5, 6-4.
Bartoli took an early lead, but was increasingly hampered by a thigh injury that required heavy strapping.
Ivanovic said that she had been unable to train properly in the 10 days leading up to New York due to an ankle injury that is still troubling her.
"I was not too happy coming into the Open with such a break, but I am just so happy that I am here and can compete," she said.
"I feel like I am playing like a top-10 player and my confidence is there, which is huge for me.
"I have a new team team around me and I have brought a lot more confidence into the US Open and the tournaments leading up to it.
On another day of soaring temperatures at Flushing Meadows, there was drama on the Grandstand Court when 10th seed Victoria Azarenka of Belarus collapsed during her tie against Argentina veteran Gisela Dulko.
With temperatures climbing into the 90s Fahrenheit (30s Celsius) for a third straight day, Azarenka quickly fell 1-5 down after 34 minutes against her more experienced South American opponent.
The 21-year-old then collapsed behind the baseline after Dulko had smacked a forehand past her and she received treatment for several minutes before retiring from the tie.
US Open referee Brian Earley said in a statement: "Victoria Azarenka retired from her match with headache-like symptoms.
"She was taken to a nearby hospital for diagnostic testing. Out of respect to her privacy we can not give any more details.
"However, we can say that this does not seem to be primarily a heat-related illness."
Dulko will next play rising Russian star Anastasia Pavlyuchenkova, who ended the hopes of Sania Mirza of India 6-2, 6-4.
The 23-year-old from Hyderabad, who is battling back after dropping out of the world top 100 due to a serious wrist injury, had raised hopes with a fine run of four wins in a row in New York coming through the qualifiers and a first-round tie against Michelle Larcher de Brito of Portugal.
But in the 20th-seeded Pavlyuchenkova, who has two title wins this year and who reached the semi-finals in Cincinnati in the buildup to New York, she came up against a big hitter who is targetting the world top 10 this year.
The only real hitch for the Russian came when she was 3-2 down in the second set and needed a medical timeout for treatment on her right forearm.
She promptly dropped her serve after that, but then ran off four games in a row to coast through.
Another seed to fall early on was Bulgarian Tsvetana Pironkova (32) who was trounced 6-4, 6-0 by Luxembourg qualifier Mandy Minella, a player making her debut in a Grand Slam tournament.