Zvonareva, who lost in the Australian Open semifinals to eventual champion Kim Clijsters, came from 3-1 down in the first set. She'll play Thai qualifier Nungnadda Wannasuk in the second round.
"It wasn't easy. I just came from the winter in Europe, so I didn't know what to expect," Hantuchova said.
Hantuchova has lost all three meetings after Date Krumm came out of retirement in 2009.