Italy's Flavia Pennetta took down the third-seeded Sharapova 6-3, 3-6, 6-4.
Sharapova was the runner-up at Wimbledon earlier this summer and was coming off a title in Cincinnati last month.
A two-time winner this year, Zvonareva will next take on Sabine Lisicki of Germany, who earned a 6-0, 6-1 victory over American Irina Falconi. Zvonareva has had a fairly strong summer after a third-round exit at Wimbledon, winning in Baku with a runner-up finish in her next event at Carlsbad and a semifinal appearance at the U.S. Open tuneup in Cincinnati. She was also a third-round loser in Toronto.
Monica Niculescu of Romania and Germany's Angelique Kerber were also early winners on Friday at Flushing Meadows. Niculescu thumped Lucie Safarova of the Czech Republic 6-0, 6-1, and will next face Kerber, a 6-3, 6-1 winner over Russia's Alla Kudryavtseva.
Other third-round matches Friday include ninth-seeded Samantha Stosur against Russia's Nadia Petrova and American Christina McHale against Russian Maria Kirilenko in the opening night match at Ashe Stadium. McHale knocked out eighth-seeded Marion Bartoli in the second round.