It marked Juve's first win for 2011.
"It was important to get the three points, especially as Milan drew 1-1 at Lecce later that evening which allowed us to close the gap to the leaders by two points," Bonucci wrote on his website.
"It was a hard game, played in a state of emergency, in which some magic from our captain and Aquilani allowed us to get the better of Bari."
On his former club, Bonucci added: "Bari showed against us that they don't deserve to be where they are in the League.
"I hope that Bari can soon start to climb the table and get the results that they have shown they merit."