AC Milan hadn’t conceded a goal for 599 minutes but Henrikh Mkhitaryan ended that record when he broke the deadlock at the San Siro after 15 minutes.
Then moments after Mkhitaryan had struck the crossbar, Aaron Ramsey doubled Arsenal’s lead with a composed finish from a Mesut Ozil pass.
Arsenal had gone four games without a win and the pressure was growing on Wenger and his players with the last result a shock defeat to Brighton.
But the result puts Arsenal in a great position ahead of next week’s second leg and ends a run of four defeats.
AC MILAN 0 – ARSENAL 2: MATCH REPORT
And Wenger admitted it was important for his side to finally overcome a difficult spell.
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He said: “It is an important win of course after we had a nightmare week.
“Overall it is important to win, but it is not qualification. We have to finish the job at home. I am happy with the spirit and response we gave.
“We were not in a position to take risks, but we could not be too cautious as you lose fluidity. We defended with resilience until the end.
“When you play in a cup final it is hard to digest in a few days.
“When you are knocked down like a boxer you don’t have time to react and you are only halfway up, but you have to respond. Your pride and desire to show quality has to come through in the game.”
On his return to the side after missing Sunday’s defeat to Brighton, Ramsey was excellent in midfield alongside Granit Xhaka and Jack Wilshere.
And the Welshman said having a good start was the key to their victory.
Ramsey said: “We started well, we got a couple of goals in the first half and we have shown we have plenty of character in the team.
“It is never easy to come to the San Siro and play AC Milan, we came here before and lost 4-0.
“We played well in the first half and moved the ball well and kept a clean sheet. We have been on a bad run, but sometimes you train hard and it does not work, but we know what we are capable of.”