Antonio Conte's side kicked off their Group E campaign by beating a nation sitting second in FIFA's world rankings.
Emanuele Giaccherini scored the opening goal after 32 minutes and while Belgium pushed hard for an equaliser in the second half, Italy's defence stood firm under pressure.
They made sure of the victory in additional time, with striker Graziano Pelle finishing off a counter-attacking move with a volley.
"In defence we moved really well and with a little more clinical finishing we could've achieved even more tonight," Bonucci told Sky Sport Italia.
"We were usually one pass away from sending the strikers clear on goal.
"We test and re-test these things over and over in training, which we do because when we get on the field, we know what we need to do."
While he had to do his fair share of defending throughout, defender Bonucci also showed off his abilities on the ball with a first-half assist.
The Juventus man picked out the run of Giaccherini with a superb aerial pass that just had enough height on it to clear the head of Belgium's Toby Alderweireld.
"I always did try that kind of pass and doing it regularly leads to improvement, as I've done it quite a few times at Juventus and now for Italy," he said.
"Fortunately, Giaccherini had that fantastic first touch for a great goal."