Goals from Henrikh Mkhitaryan, his first for the club, and Aaron Ramsey were enough to give the Gunners a valuable first-leg advantage and bring an end to their four-game losing run.
Questions over the future of manager Wenger had dominated the pre-match talk, but the 68-year-old will have been delighted with a clinical and disciplined display from his players against a Milan side who had gone 13 games without defeat.
Mkhitaryan played a key role in Manchester United's triumph in last season's tournament and he continued his fine form in continental competition with the opening goal 15 minutes in.
Milan struggled to turn their possession into meaningful chances and they were punished again seconds before the interval, when Ramsey beat the offside trap to score his seventh goal of the season.
Gennaro Gattuso's men fought hard in the second half but were comfortably kept at arm's length by the visitors, leaving them with a significant task to come at the Emirates Stadium next week.
15 - Since the start of the 2015/16 campaign, Henrikh Mkhitaryan has been directly involved in more goals than any other midfielder in the Europa League (15 - nine goals and six assists). Composed. pic.twitter.com/V08y0tTTiN — OptaJoe (@OptaJoe) March 8, 2018
Milan spurned two good openings in the first 10 minutes, with Giacomo Bonaventura just missing a cross at the left-hand post and Patrick Cutrone firing into the side-netting after escaping Shkodran Mustafi.
Hakan Calhanoglu perhaps could have won a penalty had he decided to go to ground after beating David Ospina to the ball, and Gattuso must have wished he had when the Gunners broke the deadlock.
Mkhitaryan, collecting Mesut Ozil's pass, turned past Davide Calabria and sent a shot off the boot of Leonardo Bonucci and into the net, with Gianluigi Donnarumma wrong-footed in goal.
It was the first goal Milan had conceded in 599 minutes and they should really have been punished further, with Danny Welbeck shooting straight at Donnarumma one-on-one and Mkhitaryan clipping the crossbar with the goal at his mercy.
But on the brink of half-time, Arsenal did score a second. Ozil played a fine pass into Ramsey's path and the Wales midfielder rounded Donnarumma for an easy finish.
Milan ended the first half without a shot on target and they nearly started the second by gifting Arsenal another goal, with Donnarumma doing just enough to deny Welbeck after Franck Kessie wildly kicked the ball into the striker's path.
Gattuso introduced Nikola Kalinic and Andre Silva to bolster Milan's limp attack, but speculative efforts from Bonaventura and Kessie were about the best the home side could muster, allowing Arsenal to head back to London with a solid lead and a major boost in confidence.