The second seed was given a tough time by Ukraine's Kateryna Bondarenko before finally prevailing 7-5 3-6 6-3 for an unconvincing victory.
It was clear from the off that the world number two, who lost last year's final to Kim Clijsters, was not at her best but she managed to take the first set in 47 minutes.
Things looked good for Zvonareva when she went a break up in set two but then the Russian lost four games in a row midway through the set and all of a sudden the match was all square.
However, Zvonareva refocused at the start of the decider and immediately raced into a 3-0 lead.
Although Bondraenko managed to break back to reduce the deficit to 3-4, she immediately lost her own delivery again to leave Zvonareva serving for a place in round three.
Despite missing with her first two match points, she finally closed the match out after two hours and seven minutes on the Arthur Ashe Stadium.
Zvonareva took the positives from her display afterwards.
She said: "I wouldn't say I'm pleased with the quality of tennis I showed, but I'm pleased the way I handled the match.
"It wasn't easy for me out there and she's a tricky player. I was trying to find my ways. You know, I had the lead in the second set and she was able to turn it around. I think she just went for her shots.
"It was difficult for me in the second set, but I started well the third set and then I was able to play some good rallies when I needed it in the tight moments."
Zvonareva will next play Laura Robson's conqueror, 30th seed Anabel Medina Garrigues.