The forward, who joined Massimiliano Allegri's side last week in a swap deal with Inter Milan involving Antonio Cassano, dragged his new club to victory in a match where Bologna may have felt unfortunate not to have picked up a point.
"This is a good sign for me and those who believed in me," said Pazzini as he clutched the match ball after the game. "I'm very happy, I scored goals for the team in a difficult match.
"I couldn't have asked for better than this. There are lots of good sides but Milan will definitely try to win the title."
Television replays showed both players tugging at each other's shirts but Pazzini dusted himself down and smashed home his first Milan goal from the penalty spot.
The home team's pressure was rewarded four minutes before half-time when Antonio Nocerino clumsily brought Diamanti down in the area.
Pazzini put Milan back in front with 13 minutes left when Federico Agliardi dropped a cross at the striker's feet.
Torino swept Pescara aside in the day's other game after the visitors had Christian Terlizzi sent off in the 27th minute.
