A goal in either half ensured Allegri's men took full advantage from their trip to Emilia-Romagna as they put further pressure on rivals Juventus in the title raceAC Milan have consolidated their position at the Serie A summit after casting aside Parma in a 2-0 victory at the Tardini on Saturday.
Zlatan Ibrahimovic again provided ample inspiration for his side, scoring a penalty in the first half to put the Rossoneri in the driving seat, before Urby Emanuelson wrapped up the spoils just before the hour mark to put the leaders provisionally seven points clear of second-placed Juventus.
However, it was the hosts who looked most dangerous in the early stages. Jaime Valdes and Sebastian Giovinco constructed a fine pair of moves, but they could not find the right finishes to test Christian Abbiati from close range.
Unsurprisingly, Parma were made to pay for wasting their initial hold on the match, as a speculative long ball from Antonio Nocerino paved the way for the first goal, albeit against the run of play and much to Roberto Donadoni's frustration.
Ibrahimovic laid the ball off for Emanuelson to rifle home on the volley, but Cristian Zaccardo blocked the ball with his hand, leaving the referee with no choice but to award a penalty. The Swede stepped up and slotted the spot-kick down the right-hand side, giving Milan a precious lead.
The champions began to grow in stature as the first half wore on, but wayward finishing meant the score stayed at 1-0, although Gabriel Paletta could have put a spanner in the works if his goal-bound header had hit the back of the net rather than the crossbar.
Emanuelson was then gifted with a perfect chance at the back post, but he ballooned his effort, while El Shaarawy's strike prior to half-time crashed against the post. Nevertheless, it was Milan who went into the break with the upper hand.
Parma started the second half with vigour but, just like in the first, they failed to make the most of their momentum and were hit with a fatal sucker punch.
Emanuelson made sure he put his previous miss to bed by thundering through the hosts' back line, before coolly rounding Antonio Mirante and poking the ball into an empty net to secure all three points for the visitors.
The Dutchman could have even had an opportunity of a hat-trick thanks to more inventive play from Ibrahimovic, but he could only skew his shot off target. Milan were firmly in control, and for most part of the latter stages, did not allow Parma to stage a comeback.
However, they almost did with five minutes to go, as Gianluca Musacci fired a stinging attempt at Abbiati, courtesy of an unpredictable deflection off Thiago Silva, but the former Italy shot stopper was on hand to expertly tip the ball away.
Gennaro Gattuso also made his long-awaited comeback from an eye problem, coming on to a standing ovation deep in injury time for fellow midfielder Sulley Muntari. It was the World Cup winner's first appearance since September.
The 2-0 win saw Milan temporarily move seven points clear of second-placed Juventus, who travel to Fiorentina later on Saturday. Parma, however, stay 17th and just six points clear of Lecce, who occupy the last relegation spot.