The Milan side booked their place in the semi-final after a 1-1 draw against Napoli which sees them qualify 2-1 on aggregate.
Olivier Giroud struck the crucial goal before the break to put the seven-time champions through 2-1 on aggregate and end Napoli’s historic run.
Giroud tapped in what turned out to be the decisive goal two minutes before the break after a blistering run from Rafael Leao, who was once again key as Milan beat Napoli for the third time this month.
The France striker’s 13th goal of the season saved his blushes after he missed a penalty midway through the first half.
Stefano Pioli’s side now have the prospect of a local derby in the last four as Inter Milan hold a two-goal lead ahead of their second leg with Benfica on Wednesday night.
Milan have not contested a Champions League semi-final since they were crowned kings of Europe for the seventh and most recent time in 2007.
Osimhen scored in stoppage time but it was not enough for Napoli who are creaking as they come towards the end of what has been a phenomenal season.