The Hornets were under considerable pressure as Bournemouth sought to cancel out Eliot 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 today. (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."
Despite the loss, Bournemouth boss Eddie Howe was pleased with his team's display on the back of the 5-1 drubbing at Huddersfield on Saturday, which came following their 6-1 loss at the hands of the Hornets in their previous away outing 18 days ago.
"The keeper's made a couple of good saves, we've wasted opportunities when we should have done better - a lot of crosses went into the box but unfortunately we couldn't find the missing touch we needed - but all in all it was a much better performance," the Cherries boss said.
"Certainly looking at tonight's game I think we've been slightly unlucky, but you do make your own luck.
"The needless goal that we conceded certainly gave us a mountain to climb. But at 1-0 we were bombarding their goal and they broke away and scored the second with a real moment of class and ultimately that class has decided the game."
He added: "Individually it was a good response to Saturday. I felt there were some really strong performers from people who needed to put a performance in and it was very pleasing to see them come through character-wise because it is a test, when you have a disappointing result, how do you respond to that.
"We created chances, we kept the ball very well at a tough ground. Even though they made changes, we made changes and it was still a very competitive game, so all in all I can't be too disappointed."