The former Inter Milan striker opened the scoring from the penalty spot in the 16th minute, but the Rossoblu responded well with Alessandro Diamanti scoring a deserved equaliser from the spot on 42 minutes.
But Pazzini wrapped up victory with two goals in eight minutes towards the end of the match at the Stadio Renato Dall'Ara.
The first penalty of the game was awarded when Nicolo Cherubin tugged on the shirt of Pazzini, who duly tumbled inside the area and then opened his account for the Rossoneri from the spot.
Bologna levelled through the second penalty of the game, and it was no surprise that Diamanti earned it as he was fouled by Antonio Nocerino just inside the penalty area.
He too stepped up himself to send Christian Abbiati the wrong way and bring Bologna level in the 42nd minute.
Diamanti continued to cause problems for the visitors after the break, but it was Milan who regained the lead with Federico Agliardi gifting a second goal to Pazzini.
The Bologna goalkeeper was disturbed by his own player as he went to claim Luca Antonini's deflected cross, but the ball fell for Pazzini, who swept it in from two yards.
Pazzini then completed his hat-trick in the 85th minute, cleverly guiding Nocerino's shot into the bottom corner with his back to goal.
Earlier tonight, newly-promoted Torino picked up their first win of the season with a 3-0 victory against 10-man Pescara at the Stadio Olimpico.
Alessandro Sgrigna put the Granata in front in the 34th minute, seven minutes after Christian Terlizzi was given his marching orders.
Matteo Brighi then added a second before Torino captain Rolando Bianchi wrapped up victory having missed a penalty in the first half.
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