The Gunners headed to Italy on the back of their worst run of form in 16 years, losing each of their last four in all competitions, but they produced a professional performance to come away victorious.
Chief playmaker Mesut Ozil played a direct part in both first-half goals, setting up Henrikh Mkhitaryan and then Aaron Ramsey as Arsenal put a halt to their opponents' 13-match unbeaten run with relative ease.
In the fourth two-legged affair between these traditional European powerhouses - Milan prevailing in two of those - the contest started in a frantic manner as both teams took it in turns to attack.
All either side had to show for the end-to-end battle were wayward shots from Patrick Cutrone and Mkhitaryan into the side-netting, before the Armenian international made a more telling impact on the game 15 minutes in.
After controlling the ball with his chest and cutting onto his right foot, Mkhitaryan powered a shot past Gianluigi Donnarumma via a telling touch on its way through.
The next half-hour proved to be drama free, as Milan - on a six-match winning run without conceding - failed to really make the most of possession in the final third of the field.
Then came a big moment in the tie as, moments after Mkhitaryan had clipped the crossbar in a near-replica of his first goal, Ozil slotted through Ramsey for the Welshman to round Donnarumma and roll the ball into an unguarded net.
Without a game in eight days due to the postponement of the Milan derby last weekend, an unchanged Rossoneri side were unable to put their freshness to good use.
Donnarumma raced out to deny Welbeck early in the second half, but the hosts did slowly start to enjoy some sustained pressure.
Giacomo Bonaventura fired a tame attempt down the middle for David Ospina's only real stop of the evening, before guiding the ball over the crossbar when picked out in space right on the penalty spot.
The Italian midfielder then sent a deflected effort over the bar as the Rossoneri, 13 games deep into their Europa League campaign, desperately went in search of a goal to take to London.
Milan had just that one earlier Bonaventura shot to show for their attempts on target as the final 20 minutes approached, while Arsenal failed to muster a shot of any sort after the restart, preferring instead to protect their two away goals.
Bonaventura, seemingly on a one-man mission to drag his side back into the tie, came close with an angled drive, and Ospina did well to race out and get to the ball ahead of Nikola Kalinic late on.
AC MILAN (4-3-3): Donnarumma; Rodriguez, Romagnoli, Bonucci, Calabria (Borini 79'); Kessie, Biglia, Bonaventura; Suso, Cutrone (Silva 68'), Calhanoglu (Kalinic 62')
ARSENAL (4-2-3-1): Ospina; Chambers (Elneny 85'), Mustafi, Koscielny, Kolasinac (Maitland-Niles 62); Xhaka, Wilshere; Ozil (Holding 80'), Ramsey, Mkhitaryan; Welbeck