Gianluca Mancini’s first-half header was enough to give Roma a slim lead in their Europa League quarter-final tie with rivals Roma.
Milan had previously won both Serie A clashes between the two sides this season but it is Roma who take a 1-0 lead into the second leg at the Stadio Olimpico next week.
Last season’s beaten Europa League finalists will fancy their chances of reaching a semi-final against either West Ham or Bayer Leverkusen after edging to victory at the San Siro.
The visitors started the quicker of the two teams but it was Milan midfielder Tijjani Reijnders who had the first meaningful effort of the contest as he forced a decent save out of Mile Svilar.
At the other end, Mike Maignan made a terrific stop to keep out a deflected Stephan El Shaarawy strike, although Romelu Lukaku appeared offside in the build-up.
However, Roma would take the lead from the resulting corner as Mancini slipped his defender to head in Pablo Dybala’s set-piece.
Having scored the winning goal in the derby clash with Lazio last week, the Italy defender is proving a handful at the other end of the pitch.
Milan went in search of a leveller and Olivier Giroud came close only to see two quick-fire efforts both cleared off the line by Lukaku.
An acrobatic overhead kick from Rafael Leao was off-target with Reijnders again testing Svilar before the break.
The Netherlands midfielder was again thwarted by Svilar in the Roma goal soon after the interval.
Roma skipper Lorenzo Pellegrini flashed a shot wide of the target on the hour-mark, with Bryan Cristante following suit shortly after.
Theo Hernandez and Reijnders came close for Milan as they pushed for a leveller, Svilar on hand to tip a cross-cum-shot from Yacine Adli onto the crossbar.
The hosts’ goal never came as Giroud also hit the woodwork with a marvellous late chance.
'I will keep fighting' - Ten Hag adamant he is the right manager for Man Utd
Erik ten Hag insists that he is the right man for the job at Manchester United despite their 4-0 thrashing at the hands of Crystal Palace on Monday.
Michael Olise netted twice against a sorry United team at Selhurst Park, with Jean-Philippe Mateta and Tyrick Mitchell also getting on the scoresheet.
It is the first time that Palace have done the double over the Red Devils in the Premier League, as United extended their winless run on the road to five games.
There has been a lot of speculation over Ten Hag’s future following a disappointing second campaign in charge, with just one year left on his contract.
Asked if he was the right manager for United, he told Sky Sports: "Absolutely. If the right players are there and available, we have a good squad, but are missing the whole backline – we had problems.
"I will keep fighting. I prepared the team in the best way I could do. It was not good enough, by far – I have to take responsibility for that. But I will find energy and prepare them for Sunday’s game.
"At the end of the day, I have to do it with the players who are available. All season, we have huge [injury] problems. Many times we have sorted it out. Today we didn’t."
United have struggled with injury problems all season, with Harry Maguire and club captain Bruno Fernandes joining the lengthy list of players missing against Palace.
Ten Hag highlighted the lack of defensive options at his disposal but did not make excuses for the poor performance, adding: "It’s clear and obvious – this is underperforming. It’s not good enough. We are very disappointed in this. Our fans were behind us all the way – we should have kept fighting like the fans did.
"There are always reasons. Everyone sees our backline, we have huge problems, but at the end of the day we have to deal with it – we should have done better than we did.
"We know [how damaging it could be], but we have nine points to play, so we have to fight for the nine points."
Man Utd thrashing a 'big statement' but Palace are not surprised, says Eze
Eberechi Eze says Crystal Palace's 4-0 thrashing of Manchester United is a "big statement" but insists there should be little surprise that it happened.
Micheal Olise scored twice as Palace ran riot against the sorry Red Devils at Selhurst Park on Monday.
Jean-Philippe Mateta and Tyrick Mitchell also got in on the act as Palace sealed their first league double over United.
Palace have now won four of their last five Premier League games, with Oliver Glasner having turned the tide in the past few weeks.
Speaking to Sky Sports, Eze said: "It says a lot, it's a big statement, but we're not surprised.
"We know what we're capable of, we know what we can do. The quality we've got in the dressing room is high – we don't see it as a surprise. We know what we came here to do today, it worked.
"You can see we’re creating chances, we're not worried about what's going on behind us. We're attacking, pressing, we're aggressive – we're going to continue to create chances for sure."
Also speaking to Sky Sports, Glasner said: "Congratulations to the team. I think in the first half, we didn't play as well as we could, but we were very efficient and scored very nice goals.
"At half-time, we made some adaptations, and the second half was much better. We created a lot of chances, scored some nice goals, and it's a great win.
"We know we have quality when we get our players in situations to score a goal.
"Good players, a good team spirit, but we must always stay humble. It's not so long ago we were struggling [in a relegation battle]. We are doing well, but we have a lot to improve."
This was Palace's biggest Premier League win since beating Leeds United 5-1 in April 2023, while it also marked their biggest on home soil in the competition since a 5-0 victory over Leicester City in April 2018.
Udinese 1-1 Napoli: Struggling Bianconeri grab last-gasp home draw
Napoli were held to a 1-1 draw at relegation-battling Udinese in Serie A on Monday after a stoppage-time goal by forward Isaac Success cancelled out a Victor Osimhen header.
Osimhen nodded home to give Napoli the lead in the 51st minute after Matteo Politano sent a lofted cross from the right into the middle of the box, and the Nigerian striker headed the ball in off the left post.
The Nigerian thought he doubled their advantage in the 80th minute, but his effort was ruled out for offside, before Success bundled in the leveller in stoppage time, netting from a Thomas Kristensen header.
Napoli moved up to eighth on 51 points from 35 games and are nine points behind both fifth-placed Atalanta and Roma, in sixth.
Data Debrief:
Osimhen is the third Napoli player to score in six matches in a row against a single team in Serie A in the three-points-for-a-win era, after Gonzalo Higuain against Lazio between 2013 and 2016 and Dries Mertens against Bologna between 2016 and 2019.
Despite fighting back to earn a point, Udinese have now failed to win three games under a new manager for the first time since August-September 2010 under Francesco Guidolin.
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