The Hornets were under considerable pressure as Bournemouth sought to cancel out Elliot Ward's 15th-minute own goal when they were caught out on the counter-attack. Javier Acuna fed Battocchio, who beat Ryan Allsop with an exquisite chip from the edge of the area.
Zola said: "That was something special and I'm pleased Cristian has scored that goal because he's played a good game and he worked so hard and got what he deserved.
"We can enjoy this game, this victory and we also have to say thank you very much to Jonathan (Bond) because he was exceptional. (From) a couple of opportunities he was really unbelievable."
The Hornets goalkeeper, who made at least three top-class saves, was one of 10 changes from Sunday's draw against Nottingham Forest.
Zola added: "It was a good performance, but I know I can make the changes because the squad is quite strong. Even if I make changes I still have a good side. If you see the defenders, some of them could be regulars so it's good for me that I can make changes so it will keep everyone fresh and everyone on the spot."
Watford's reward for the victory was another home tie against Norwich in the next round and Zola was delighted with the draw.
"That is a good draw for us," he said. "It's a Premier League club, it's what we wanted. We're going to have a good go at them and I'm pleased."