Mkhitaryan powered a deflected shot past Gianluigi Donnarumma for the opening goal 15 minutes in, before Ramsey kept his composure by rounding the young goalkeeper and slotting the ball home.
Milan, unbeaten in 13 games prior to this evening, could not muster a response in the remainder of the match to give the Gunners a huge advantage ahead of the return fixture.
Relive how the 90 minutes of action unfolded with Sports Mole's live text coverage below.
STARTING XI: Ospina; Chambers, Mustafi, Koscielny, Kolasinac; Xhaka, Wilshere; Ozil, Ramsey, Mkhitaryan; Welbeck
SUBS: Cech, Holding, Maitland-Niles, Elneny, Iwobi, Nelson, Nketiah
STARTING XI: G.Donnarumma; Rodriguez, Romagnoli, Bonucci, Calabria; Kessie, Biglia, Bonaventura; Suso, Cutrone, Calhanoglu
SUBS: Kalinic, Silva, Borini, Zapata, Montolivo, Locatelli, A.Donnarumma
Genaro Gattuso: "I've been through games like this as a player, everything is different now. Compared to Wenger I'm a rookie, I'm just starting and he's been coaching for 30 years. We're preparing, Arsenal are a technical team that doesn't like defensive transitions. We'll have to do well not to suffer from what they do, and then make them run when we have the ball. We can't make mistakes and we need to keep our composure. We must not be afraid of the 70,000 fans that will be at San Siro and show our qualities, both technical and physical. We must make it very difficult for them."
Arsene Wenger: "It makes me think a little bit about last year. Last year with the FA Cup, we made 75 points in the league and missed the Champions League by one point only. Seventy-five points is still a very good score what we will not reach this season. [The Europa] is an opportunity we have to take. It increases the pressure even more on this competition. It is certainly difficult when you go through a patch like we are but I believe it is a good opportunity to show you have the quality and strength. You can only show that when it is difficult. It is a good opportunity to show we can deal with that and as well, on the longer term, it will make the team even stronger."
AC MILAN SUBS: Kalinic, Silva, Borini, Zapata, Montolivo, Locatelli, A.Donnarumma
ARSENAL SUBS: Cech, Holding, Maitland-Niles, Elneny, Iwobi, Nelson, Nketiah