Unbelievably, though, the Dutchman who cannot stop scoring chose the wrong option and his attempted dink went straight into the arms of relieved Milan goalkeeper Christian Abbiati and with it Arsenal's best chance of staying in the competition.
The incident early in the second half proved a pivotal moment in the match as Arsenal, who had roared into a 3-0 halftime lead, ran out of steam and Milan held on for a 4-3 aggregate victory to move into the quarter-finals.
"All that really mattered was the result and that we got through to the next stage," relieved Milan coach Massimiliano Allegri told reporters.
"Today was in some ways the match of the season for us because now we are among the best eight teams in Europe and that has not happened to Milan for a few years."
"Right now, although we lost I am very happy, I am delighted we've qualified and that was the main objective, although we have to play better than that."
Arsenal manager Arsene Wenger was left to rue the one that got away but he was full of praise for the Milan keeper.
"What can I say?" he told reporters about the chance spurned by Van Persie whose 32 goals in all competitions this season, including a penalty against Milan before the break, have lit up the club's otherwise stuttering season.
"The one you would want the chance to go to is Van Persie. But he wanted to chip the keeper. You have to give credit to Abbiati, he came up so quickly, it was a fraction.
"Players have to make decisions so quickly. If he scores it's great, but credit to the keeper," added Wenger.
Milan had suffered a fright night until that moment as their 4-0 lead from the first leg almost evaporated with Arsenal scoring through Laurent Koscielny, Tomas Rosicky and Van Persie.
After Van Persie missed the chance to put a rampant Arsenal 4-0 up, however, Milan finally woke from their slumber and could have put the tie to bed on several occasions.
As it was, squandered chances by Zlatan Ibrahimovic and Antonio Nocerino did not in the end prove costly as the Italians reached the last eight for the first time since they won the trophy for the seventh time in 2007.
MILAN SUFFER
It was too close for comfort, though, for Allegri, who spent most of the first half gesticulating furiously from the touchline.
"When we went two behind, we were not in control and credit must go to Arsene for how Arsenal played in the first half," he told reporters.
"We suffered in the first half after conceding a goal in the first few minutes and all credit to Arsenal because I knew the first half was going to be tough and they made it hard for us.
"But we played very well in the second half and only gave them one real chance in the second half."
He said his side would have to improve if they were to challenge the Spanish axis of Barcelona and Real Madrid for Europe's most prestigious c
