Hakan Calhanoglu's long-range striker had given Milan a 1-0 lead on the night going into half-time, but the England worldwide striker went down in the opposition's area under minimal contact from Swiss defender Ricardo Rodriguez to earn a spot-kick before the break - before dispatching the opportunity to bring the hosts level.
Granit Xhaka then put us firmly in control with a long-range effort before Welbeck sealed a 5-1 aggregate victory with a late header to book our place in today's quarter final draw.
While Arsenal have struggled in the Premier League over recent months, they have now reached a European quarter-final for the first time since 2010.
Wenger, speaking about Welbeck's penalty decision, said: "When I watch the penalty, I will give you an honest answer. I never gave up hope of getting back in there", The Arsenal midfielder said in the post-match interview. The side drawn first will play the first leg at home.
Swedish referee Jonas Eriksson certainly was but he was also left hung out to try by the extra official on the touchline, Stefan Johannesson, who was just a few yards away but still saw something that no amount of TV replays failed to show. I don't know. The Italian players were unhappy with it.
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Arsene Wenger has promised to give Danny Welbeck a piece of his mind if he judges that he dived to win Arsenal's crucial penalty, despite claiming not to have seen the incident. "We don't think it's bad but he cramped up and couldn't go on". I can understand that, but I don't know what happened.
Arsenal's Danny Welbeck scores their first goal from the penalty spot.
Remarkably, it was Welbeck's first penalty in senior football but Wenger had no qualms about him taking it. We are happy to be through to the next round and we will see who we get.
The team we all want to avoid is Atletico Madrid as they are easily the best side we could draw after the Spaniard's thrashed Lokomotiv Moskow 8-1 on aggregate.
The draw for the quarter-finals of the Europa League will be made at 1200 GMT/17.30 IST on Friday at the UEFA headquarters in Nyon, Switzerland, directly after the Champions League quarter-final draw.