The Rossoneri triumphed 4-2 over Torino - climbing to seventh in the Serie A in the process - with four separate goalscorers on the scoresheet.
The Turin-based hosts went ahead in the 28th minute, but its second strike came after a flurry of four goals from Robinho, Antonio Nocerino, Giampaolo Pazzini then Stephan El Shaarawy.
The Rossoneri victory leaves them seventh in the table and five points off fourth-placed Roma, which has 29 points, along with Fiorentina and Lazio which lies in fifth and sixth places respectively on goal difference.
"It was an important victory, which followed up the previous win. We went behind to a technical error, but we did well to deserve the win," Allegri told Sky Sports Italia.
He added, "We could have done better in the first half where we lacked a bit of speed and did not reach the placement of midfielders.
"We are moving closer to the top six in the standings, and it was important to win today, also considering the result of Roma last night."