The Italians thought they had taken an early lead when Rafael Leao broke clear to fire past Dean Henderson – but the forward was ruled offside.
Milan had the ball in the net again in the 11th minute when Franck Kessie slotted in after a throw-in, but this time the goal was ruled out following a VAR review for handball in the build-up.
Diallo replaced Anthony Martial for the second half – and the 18-year-old made an instant impact as he flicked home a quick free-kick from Bruno Fernandes to head United in front in the 50th minute.
Amad Diallo (centre) headed Manchester United in front at Old Trafford (Martin Rickett/PA)
Rory McIlroy, centre, has no plans to split with caddie Harry Diamond, left (Kenny Smith/PA)
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Defending champion Rory McIlroy has no plans to change his caddie or coach and feels his best is yet to come as he seeks the “spark” missing from his game at The Players Championship.
McIlroy admitted he was somewhat dejected after a final round of 76 in the Arnold Palmer Invitational on Sunday and spoke about “maybe looking to go in a different direction”.
“We’re disappointed but I can take a lot of positives from it, especially the first hour of the performance.
“I think Allan had a big chance when it was one each and unfortunately (David) De Gea saved it.
“But for long periods I was pleased but we’ve got to put the whole thing together and get a few results, of course.”
Asked how big the threat of relegation is after Fulham cut the gap by beating Sheffield United on Saturday, Bruce said: “Well, look, there’s six or seven teams in and around us with 13 games to go.
Ole Gunnar Solskjaer plays down talk of a Manchester United title challenge eveningtelegraph.co.uk - get the latest breaking news, showbiz & celebrity photos, sport news & rumours, viral videos and top stories from eveningtelegraph.co.uk Daily Mail and Mail on Sunday newspapers.
“Of course we’ve added that spark I think but also when you get results, and things are going your way, that helps.
“We brought it up early on in pre-season that we need to add more points towards the end of games. That’s something we do as a club – we’ve done that so many times and we’ve done that quite a few times this season as well.
“Physically we last games more. I have to say I feel a bit for Wolverhampton, they have had one recovery day, which I don’t think is right for any player or any team to only have one day between games.