A lightning-quick start saw Malick Thiaw keep the ball alive at the far post, and after he headed back across goal, Feyenoord old-boy Santiago Gimenez rose highest to head home just a month after his move from Rotterdam.
It was largely one-way traffic towards the Feyenoord goal up to half-time, and Joao Felix almost edged them ahead in the tie, when his wicked strike forced an impressive save out of Timon Wellenreuther.
The Dutch side did incredibly well to regain their composure at the San Siro, but still needed to come out fighting in a cauldron of noise. And they almost got caught in transition when Rafael Leao ghosted in behind Givairo Read, but Wellenreuther denied him at his near post to keep the scores level on aggregate.
Milan were in the ascendancy throughout the opening stages of the second half too, but their chances of progression inside the 90’ took a blow when Theo Hernandez dived in the area and was dismissed for a second bookable offence.
Milan completely lost their momentum after that red card, and although Feyenoord had offered precious little in the final third all evening, they found a moment of quality a little under 20 minutes from time.
Hugo Bueno was afforded the freedom of the San Siro on the left, and he planted an inch-perfect cross onto the head of Julian Carranza, who powered home from six yards.
It was a remarkable show of courage from the youngest Feyenoord team ever to take to the field in a European game.
The question remained whether Feyenoord’s inexperience would show in the closing stages, and with a man advantage they were looking every bit like a side with a wealth of UCL experience.
The Dutch side were relieved to see only five minutes go up on the stoppage time board, and that proved to be the incentive they needed to reach the last 16 of Europe’s premier club competition for the first time in 50 years.
Seven-time winners AC Milan, meanwhile, will now have to focus on their Serie A campaign to get into next season’s Champions League.