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."
Elsewhere, Torino picked up their first victory by beating 10-man Pescara 3-0.
Milan opened the scoring at Bologna after 16 minutes when Pazzini raced through on goal and was controversially adjudged to have been brought down in the area by Nicolo Cherubin.
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.
Bologna responded by taking the game to Milan, with the impressive Alessandro Diamanti at the heart of their attacking play.
The home team's pressure was rewarded four minutes before half-time when Antonio Nocerino clumsily brought Diamanti down in the area.
Diamanti then smashed the penalty past keeper Christian Abbiati to equalise.
DIAMANTI MOVEMENT
Kevin Prince Boateng drove Milan forward in the second half but Diamanti also continued to cause the visitors problems with his passing and movement.
Pazzini put Milan back in front with 13 minutes left when Federico Agliardi dropped a cross at the striker's feet.
The new striker, who made his debut as a second-half substitute in the 1-0 home defeat by Sampdoria on Sunday, clinched victory in the 85th minute, when he touched in a wayward Nocerino shot.
Torino swept Pescara aside in the day's other game after the visitors had Christian Terlizzi sent off in the 27th minute.
Terlizzi was dismissed for bringing down Rolando Bianchi in the box and the striker missed the resulting penalty.
Alessandro Sgrigna (34 minutes), Matteo Brighi (59) and Bianchi (63) were on target for Torino.
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