After a bright start from AC Milan, it was Arsenal who took the lead in the 15th minute through Henrikh Mkhitaryan whose right foot shot took a slight deflection before ending inside the net.
In the fourth minute of first half added time, Aaron Ramsey made it 2-0 off a brilliant through pass from Mesut Ozil as he rounded Gianluigi Donnarumma before slotting into an empty net.
The defeat ended Milan’s 13-game unbeaten run.
The last time Arsenal won at the San Siro was a 2-0 win in the second-leg round of 16 of the Champions League in 2008.
Also on Thursday night, two-time Europa League winners Atletico Madrid (2010, 2012), defeated visiting Lokomotiv Moscow 3-0.
Goals from Saul Niguez, Diego Costa and Koke in the 22nd, 47th and 90th minutes gave Atletico a comfortable first-leg win.
In other results, Dortmund were stunned at home 2-1 by Austrian side Salzburg while Lyon pipped CSKA Moscow 1-0 in Russia.
Super Eagles star Ahmed Musa was in action for CSKA Moscow and played for 90 minutes.
All the return legs come up on Thursday, March 15.
AC Milan 0 vs 2 ArsenalAtletico Madrid 3 vs 0 Lokomotiv Moscow
Borussia Dortmund 1 vs 2 Salzburg
CSKA Moscow 0 vs 1 Lyon