The Italian side, trailing 2-0 from last week’s first leg, were playing their way back into the tie when they pulled a goal back 10 minutes before half-time, only to concede a controversial penalty after Arsenal striker Danny Welbeck went down from a ‘ghost’ challenge before scoring from the spot.
Maybe Arsenal manager Wenger was right when he recently commented that English forwards have mastered the art of diving.
Either way it should not detract from the fact Arsenal were the best team over the two legs.
And Welbeck scored a good second goal late on to seal the deal. By then they had given themselves an even bigger cushion when a goalkeeping error gifted Granit Xhaka Arsenal’s second on the night in the 71st minute.
The teams Arsenal could face in the last eight, as they bid to win the trophy and secure a place in next season’s Champions League, include Atletico Madrid, Marseille, Lazio, Sporting Lisbon, and RB Leipzig.
A capacity crowd and a fervent visiting Milan support ensured this match did not feel like a second rate European tie as two teams struggling to match their former glories went into battle for the first time in five years, when the Italians won.
And it was Milan who showed first as on-loan Sunderland man Fabio Borini went on an overlapping run down the right and pulled inside for Andre Silva, who shot into the side netting.
It was close enough for sections of the crowd to think Milan had scored with only a minute on the clock.
Arsenal recovered quickly and Laurent Koscielny headed over the bar from a Henrikh Mkhitaryan corner to mark Arsenal’s first attempt on target as Wenger’s team began to look like turning possession into chances.
Unfortunately, for Arsenal and the France international, he landed awkwardly after twisting through the air and was substituted soon after, making way for Calum Chambers with 11 minutes gone.
Not that Arsenal had too much to worry about at the back, as they looked to use attack as the best form of defence.
They were also boosted by the return of full-backs Nacho Monreal and Hector Bellerin ahead of schedule following injury.
Koscielny’s early exit also shown the spotlight more on midfielder Jack Wilshere, who marked his return to the senior England squad by taking on the captain’s armband.
But it was fellow England international Welbeck, a surprise reselection in Gareth Southgate’s latest pre-World Cup squad yesterday, who threatened next as he ended a blistering run with a powerful shot which was too close to Italian wonderkid keeper Gianluigi Donnarumma.
The game came to life 10 minutes before half-time when there was a goal at either end within a matter of minutes. First the Turkish striker Hakan Calhanoglu scored a super strike from 30 yards to leave David Ospina no chance to save with a dipping right foot effort into the bottom left hand corner of the net.
Then, with the Milan supporters still deliriously celebrating their lifeline goal, Welbeck won Arsenal a penalty with what looked like a dive at first glance.
It was enough to convince the Swedish additional assistant referee behind the goal, Stefan Johanesson, who signalled for spot kick.
The defiant official did well to stand his ground from an avalanche of manic Milan protests as all of their players clearly thought the Arsenal man had conned the official.
Welbeck, once he had got up from his acrobatics, also stood his ground, though, and sent Donnarumma the wrong way from eh spot to record his first goal of any description since January and first in Europe for three years.
Milan and their animated manager Gennaro Gattuso nearly exploded with rage on the touchline.
He was just as irate when his side were denied a penalty of their own for what appeared like a Chambers handball in the very next attack.
We've completed our Italian Job ✅— Arsenal (@Arsenal) March 15, 2018
And that means we're through to the Europa League quarter-final 👊 pic.twitter.com/ogPYR9MQwl
Wilshere then had a wonderful effort saved by a full stretch Donnarumma and both teams left the field to a standing ovation at the break.
That Welbeck goal, however, had effectively killed off the tie and Milan rarely threatened after the break, despite Patrick Cutrone missing a sitter with the score still at 2-1.
It was soon after that when Xhaka’s speculative shot squirmed into the net off an embarrassed Donnarumma with 19 minutes to go.
Welbeck then rubbed a huge dose of salt in Milan’s gaping wound when he headed in an easy second of the night in the closing minutes.
Arsenal do not play again until after the international break when they host Stoke on 1 April.
The doom merchants still talk of a grave future for the north London club as they struggle to keep up in the league, but the fact they are the only London club left in Europe – following the exit of Tottenham and Chelsea in the Champions League - will keep them smiling for a few days yet.
Koscielny (Chambers 11), Mkhitaryan (Elneny 69), Ozil (Kolasinac 79)
Cech, Iwobi, Maitland-Niles, Kolasinac, Nketiah.
Cutrone (Kalinic 67), Calhanoglu (Bonaventura 70), Kessie (Locatelli 79)
Storari, Zapata, Biglia, Musacchio.
Jonas Eriksson (SWE)
Dortmund drew 0-0 with Red Bull Salzburg, so the Austrian side’s 2-1 victory in Germany was enough for them to advance, with Lyon losing 3-2 to CSKA Moscow at home and exiting on away goals.
French kingpins Lyon lost 3-2 to CSKA Moscow at home and exit the competition on away goals.