Milan's 4-0 win in the San Siro left Arsenal with a five percent chance of survival, according to manager Arsene Wenger, but his team struck three times in a barnstorming first half to threaten the greatest of European Cup escapes.
The Serie A champions were shocking in the first half as goals from Laurent Koscielny, Tomas Rosicky and a Robin van Persie penalty meant their lead all but evaporated.
Milan, who have won the trophy seven times, came to their senses after the break to win the last 16 tie but their fans, aware of a similar second-leg collapse against Deportivo Coruna in 2004, had their nerves shredded on a night of raw tension.
Van Persie, who scored a superb late winner against Liverpool last weekend, botched a glorious chance to level the tie early in the second half when he scooped an effort straight into the arms of Christian Abbiati and Arsenal ran out of steam.
Milan could have made it a more comfortable night but Zlatan Ibrahimovic and Antonio Nocerino were guilty of spurning the chances to give their side some breathing space.
"Right now, although we lost I am very happy," Milan coach Massimiliano Allegri told reporters. "I am delighted we've qualified and that was the main objective, although we have to play better than that."
VERY CLOSE
It was all rather an anti-climax in the end for the home side who had Milan on the ropes by half-time, leaving Wenger to rue the damage done in the away leg last month.
"We are disappointed because we touched qualification, we had the chances, and although we didn't do it, we were very close," he told reporters.
"We restored some pride after the first tie but unfortunately we are out. We had the chances but we paid the price for the first game.
"We suffered a lot physically in the second half but the players gave a faultless performance."
Premier League victories, including a 5-2 defeat of Tottenham Hotspur from 2-0 down and another comeback in a 2-1 win at Liverpool on Saturday, had fuelled belief that all might not be lost against the Italian aristocrats.
Milan made a sluggish start, inviting Arsenal forward, and it was clear they were in for a rough ride when Koscielny peeled away from his marker to meet Alex Oxlade-Chamberlain's inswinging corner with a thumping header past Abbiati to raise the volume in the stadium.
Allegri packed his Milan side with attacking menace in the shape of Ibrahimovic, Robinho and Stephan El Shaarawy, hoping to snatch the away goal that would have proved fatal for the Gunners, but they hardly got a kick as a red tide swept in the other direction.
Van Persie twice tested Abbiati, forcing one flying save, before Arsenal's second goal arrived after 26 minutes.
Theo Walcott sped down the right and his low cross was only half cleared by Thiago Silva straight to the lurking Czech Rosicky who steered a precise shot inside the near post.
