The second-seeded 2010 U.S. Open and Wimbledon runner-up Zvonareva zipped past France's Stephanie Foretz Gacon 6-3, 6-0 at Armstrong Stadium.
The Russian Zvonareva was dismantled by Kim Clijsters, 6-2, 6-1, in last year's lopsided U.S. Open finale.
Meanwhile, 22-year-old Romanian Alexandra Dulgheru, ranked 48th in the world, stunned the fifth-seeded Kvitova 7-6 (7-3), 6-3 at the USTA Billie Jean King National Tennis Center, which was in terrific shape after weathering Hurricane Irene over the weekend. Kvitova piled up 52 unforced errors en route to her early exit.
The Czech Kvitova upended Russian star Maria Sharapova in last month's Wimbledon finale, but has gone just 2-3 since capturing her first career major championship.
Thirteenth-seeded Chinese Peng Shuai doused American Varvara Lepchenko 6-3, 6-4, while 19th-seeded Julia Goerges leveled fellow German Kristina Barrois 6-3, 6-2 and 27th-seeded Czech Lucie Safarova overcame Slovakian Magdalena Rybarikova 2-6, 6-3, 6-2.
Sixteen-year-old Madison Keys dismissed 37-year-old Jill Craybas 6-2, 6-4 in an all-Ammerican affair.
Additional opening-round wins came for Brit Laura Robson, Spaniard Laura Pous- Tio and Romanian Monica Niculescu.
The top seed here is last week's New Haven titlist Caroline Wozniacki, the 2009 U.S. Open runner-up to Clijsters, who had won the last two titles here in Flushing but is missing this year's fortnight because of injury.
This year's U.S. Open singles champ will pocket at least $1.8 million, and U.S. Open Series winner Serena Williams, seeded 28th, has a shot at earning a record $2.8 million in the Big Apple. The three-time U.S. Open titlist Serena has won her last 12 matches overall and is considered one of the favorites in New York.