The Gunners travelled to the San Siro having lost six of their last eight games, but the first leg of their round-of-16 clash will help change the mood in north London following goals from Henrikh Mkhitaryan and Aaron Ramsey.
The two teams will meet for the second leg at the Emirates Stadium next Thursday, when the Gunners will seek to complete the job they started in Milan in a tournament that represents their last shot at silverware this season.
Arsenal manager Arsene Wenger was forced to shuffle his defence as full-backs Hector Bellerin and Nacho Monreal missed out through injury, with Calum Chambers and Sead Kolasinac filling on the right and left, respectively.
Danny Welbeck replaced cup-tied Pierre-Emerick Aubameyang up front with Alexandre Lacazette injured, while AC Milan boss Gennaro Gattuso named the same team that beat Lazio on penalties in the Coppa Italia on February 28.
Arsenal brought an end to Milan's run of six consecutive clean sheets in the 15th minute when Mkhitaryan found space on the left side of the hosts' box, cutting inside before seeing his deflected effort beat Gianluigi Donnarumma.
Mesut Ozil deserved credit for his perfectly floated ball over the top to the Armenia international, whose run of success in Europe continued thanks to his first goal in Arsenal colours, per Match of the Day:
Arsenal's breakthrough helped set the tone in part for the remainder of the half. The second goal would be crucial to preserving their European hopes, too, as a loss in Italy would have seen the Gunners lose five times in a row for the first time since 1977, per Daniel Damian of AllArsenal.com.
Rossoneri captain Leonardo Bonucci came within inches of equalising before the break but could only divert his header from a corner wide of Arsenal's goal after David Ospina failed to claim the ball in the air.
Mkhitaryan should have made it 2-0 before half-time after being picked out on the left once more, but he lifted his attempt just too high and struck the crossbar.
But Ramsey made up for that miss deep into first-half injury time, and Ozil was again the architect. He threaded the ball through, and the Wales international showed superb calm to dummy Donnarumma and finish into an open goal, per ESPN FC's Mattias Karen:
Welbeck almost pounced on a calamitous, looping Franck Kessie pass back to his goalkeeper for Arsenal's third just after the restart, but the Ivorian midfielder was let off the hook as Donnarumma came to the rescue.
Giacomo Bonaventura had an opportunity to get Milan off the mark at the other end not long after, but he could only lift Davide Calabria's cut-back over Ospina's bar from 12 yards out.
The second half was a messy affair for both teams, and Gattuso threw on strikers Andre Silva and Nikola Kalinic a little after the hour mark in place of Patrick Cutrone and Hakan Calhanoglu, respectively.
Wenger looked to shore up his defence by throwing centre-back Rob Holding on in place of Ozil, and James Benge of the Evening Standard took note of the Germany international's impact as he departed with 10 minutes remaining:
Former Liverpool forward Fabio Borini was Gattuso's last introduction, but a lack of cohesion between Milan's midfield and attack meant they continued to miss out in terms of clear-cut chances.
Seeing the final minutes of the game out with the ball in possession played into the hands of the Gunners, who were happy to sit back with two away goals ahead of next week's second leg.
Wenger will have also been pleased to learn Borussia Dortmund fell 2-1 at home to Red Bull Salzburg in the first leg of their last-16 encounter, potentially setting the wheels in motion for one of their major title contenders to bow out.
The Rossoneri will be chasing the goals when they travel to north London for the return leg next Thursday, while England's last remaining Europa League representatives will fancy their chances of progressing.