The result moved the Rossoneri to within four points of league leaders Inter Milan, while AS Roma remain two points behind fourth-placed Atalanta as their quest for Champions League football next season continues.
The first half was emblematic of football's quirky nature, as a 45-minute spell could have easily ended with AC Milan leading 4-3 only finished with Frank Kessie giving the Rossoneri a 1-0 lead from the penalty spot.
Roma responded right at the start of the second half when Jordan Veretout curled a beautiful effort past Gianluigi Donnarumma to restore parity in the 50th minute.
AC Milan, however, swiftly retook their lead in the 58th minute when Ante Rebic rifled the ball in after Pau Lopez had given the ball away.
Roma had plenty of chances of scoring the equaliser, but AC Milan rode their luck, although the Rossoneri did have their fair share of chances too. Stefano Pioli's men eventually saw out the game to grab three crucial three points and stay alive in the title race.
On that note, let's have a look at the five major talking points in the game:
#1 VAR comes to the fore again
On a weekend when all the headlines were occupied by referee Daniel Orsato being allowed to speak to the media and explain past mistakes, it was inevitable that the VAR would take centre stage once again.
The previous fixture between AC Milan and AS Roma - a 3-3 draw - had its fair share of controversial decisions, and there was a hint of that in this game too.
Fazio's foul on Davide Calabria would be described as soft by most referees. But there was only going to be one result once the VAR asked referee Marco Guida to check his monitor.
Further controversy came about late in the game when Henrikh Mkhitaryan tussled with Theo Hernandez in the box. But Guida booked the Armenian for simulation. One could argue that the Giallorossi midfielder received more contact than Calabria, but a foul seemingly went the wrong way.
Yet, as Orsato stated, VAR is beneficial in the grand scheme of things, and both teams would much rather it exist than not.
#2 Profligate AC Milan almost pay the price
Despite the victory, Stefano Pioli ought to walk away with a fair few concerns about the finishing from his forwards. Much like in the games against Inter Milan and Red Star Belgrade, AC Milan's forwards did not look like scoring all night, spurning chance after chance despite moving into great positions.
Even Zlatan Ibrahimovic, who ought to take his own advice to LeBron James and 'focus on the football', could and should have made it a far more comfortable night for AC Milan. Pau Lopez was well worked in the Roma goal, to be fair, but he mostly made regulation saves.
Ante Rebic spent most of the night hammering Pau Lopez' near post to no avail. He scored after deciding to try his luck with the opposite bottom corner. His manager will need more of that if AC Milan are to win the title.