The match was one of the competition’s last 16 first leg ties.
Manchester United’s Premier League rivals Arsenal and Tottenham Hotspur meanwhile tuned up for their meeting in Sunday’s north London derby with comfortable wins.
Arsenal won 3-1 at Olympiacos, while Spurs were 2-0 winners at home to Dinamo Zagreb.
The 18-year-old Ivorian Diallo joined Manchester United from Atalanta in January and scored in his second substitute appearance with a clever back-header five minutes after his half-time introduction.
AC Milan had two goals disallowed early on but Simon Kjaer’s last-gasp header ensured parity going into the second leg.
Manchester United and AC Milan have been continental champions 10 times between them but must currently make do with Europa League football.
But both sides are on course to return to the elite UEFA Champions League next season even if they trail their respective derby rivals Manchester City and Inter Milan domestically.
“We are working to grow and bring AC Milan back where we belong,” said coach Stefano Pioli. “These are the best games in that sense. So, I was happy to face a team like Manchester United.”
Manchester United returned to action after the high of their weekend derby win over Manchester City but were flat until Diallo scored shortly after the restart.
Bruno Fernandes chipped over the defence and Diallo reacted superbly to loop a header over Gianluigi Donnarumma for his first professional goal.
The youngster was signed for a reported 37 million pounds (51.7 million dollars) having played less than 90 minutes of senior football.
“He’s a great young lad and did really well after he came on,” Manchester United’s Harry Maguire said of Diallo.
“He obviously got the goal which was great to see. He did well and hopefully there’s a lot more to come from him.”
Manchester United’s best chance of the first half fell to Maguire who struck the post at a corner-kick after AC Milan dominated the early stages.
Rafael Leao’s opener for the guests was rightly ruled offside and Franck Kessie’s fine strike suffered a similar fate for handball after video review.
AC Milan finally had a goal count two minutes into injury-time from Kjaer’s header at a corner-kick which left goalkeeper Dean Henderson looking poor.
“We’re very disappointed to concede with one of the last kicks of the game,” Manchester United manager Ole Gunnar Solskjaer said later on.
“That makes it harder of course, but it was always going to be down to the second game there anyway.”
Harry Kane struck in either half, for a season tally of 26, to boost manager Jose Mourinho, who could still salvage a positive season for his Spurs side.
They have recently fallen down the English Premier League (EPL) table.
They are seventh, five points off the UEFA Champions League spots, but going into the derby seven clear of Arsenal, who have only the Cups left to look forward to in their campaign.
“We had some ups and downs in the season but we come into an important period now and it is good to feel the players are ready to help the team,” said Spurs goalkeeper Hugo Lloris.
“If we work well as a team, we will give our talent more power to make the difference.”
Olympiacos’ Youssef El Arabi equalised Martin Oedegaard’s opener, but Gabriel and Mohamed Elneny struck late to secure the away win.
The Greek side eliminated the Gunners from the competition last season with a thrilling comeback in London in the last 32 and must now undertake a similar task.
“It is a big win for us, a great result with three goals away from home and a win in this competition is always good,” said Odegaard.
“We have a big game on Sunday and then have to be ready for next Thursday.
“It is very important, we are not where we want to be in the league so this is very important for us and a chance to get UEFA Champions League football next year.”
Ajax, another former European champions, beat Switzerland’s Young Boys 3-0 while Villarreal are almost through after a 2-0 win at Dynamo Kiev.
Fellow Spaniards Granada could continue their maiden European campaign into the last eight having beaten 10-man Molde 2-0.
Roma are also well placed, having thrashed Shakhtar Donetsk 3-0.
Steven Gerrard’s new Scottish champions Rangers meanwhile will welcome Slavia Prague in the only return leg which starts all-square next Thursday after a 1-1 draw in the Czech Republic.
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