Zvonareva, the 14th-ranked defending champion, rallied from 3-5 down in the second set to win, improving her career record against her Austrian rival to 4-0.
Bammer won the Pattaya Open title in 2007.
Zvonareva benefited from a flurry of unforced errors from her opponent and cruised through the first set in 27 minutes.
In other matches, Tamarine Tanasugarn of Thailand defeated Ana Chakvetadze of Russia 6-1, 6-4.
"I have to thank fans for coming here and giving me support," Tamarine said. "I played quite consistently and tried to finish points. I was lucky though, because she just came back from an injury and was not at her best level.",
Tamarine will play Sesil Karatantchev, who managed a 7-5, 4-6, 7-5 victory over Ekaterina Bychkova.