Having sold Zlatan Ibrahimović and Antonio Cassano this summer, and then seeing strikers Robinho and Alexandre Pato pick up injuries, Milan needed the former Inter player to have an immediate impact.
And that he did, scoring his first Milan goal after just 16 minutes when Nicolò Cherubin brought him down in the box and Pazzini picked himself up and scored from the resulting spot kick.
Bologna fought level before the break, when the skilful Alessandro Diamanti was sent tumbling by Antonio Nocerino after a clever turn. He too converted his spot-kick equally emphatically.
A draw looked likely as a tight second half wore on, until Pazzini was presented with his second of the night 13 minutes from time, Federico Agliardi spilling a cross at the striker’s feet. Eight minutes later Pazzini brilliantly redirected Nocerino’s dragged shot with a bottom-corner backheel to put Milan out of sight.
Elsewhere, goals from Alessandro Sgrigna, Matteo Brighi and Rolando Bianchi earned Torino a 3-0 win at home to Pescara, extending the promoted side’s unbeaten start.