The home side knew that a draw or a win would put them through to the knockout stages, but only victory would send Ajax into the last 16.
Ajax dominated the match, but were unable to find the back of the net, enabling Milan to progress from the group.
Here, Sports Mole takes a closer look at the events that unfolded at the San Siro.
On Target 1
On Target 5
Was the result fair?
From the moment that Montolivo was sent off, Ajax had complete control of the game, but they were unable to make their dominance count. They may have had 25 shots on goal, but many of those attempts were from long range and failed to test Christian Abbiati. Milan may not have seen much of the ball, but they deserved a clean sheet for their committed defensive performance.
AC Milan's performance
Milan didn't start the game strongly and things were made worse for them just 22 minutes into the match when Montolivo was given his marching orders. They were put under a huge amount of pressure by Ajax, but did remarkably well to keep a clean sheet. Their defenders dealt with the constant threat brilliantly and Massimiliano Allegri will be delighted that his team came together to ensure their passage through to the last 16.
Ajax came into the game looking for a goal that would send them through, and completely dominated the possession against the 10 men. They may have come close by hitting the post and forcing Abbiati into a good one-handed save early on, but they lacked a cutting edge in the final third. Too many of their crosses went astray and they only managed five accurate attempts on goal.
Sports Mole's man of the match
Mario Balotelli: Milan's defence may get all the plaudits, but on countless occasions during the match, Mario Balotelli was a key outlet. He held onto the ball brilliantly, relieving the pressure on his teammates, and never stopped battling. His temper looked as though it may of got the better of him at one stage, but he kept his cool and was crucial to his side's gameplan this evening.
Montolivo made the biggest mistake of the night by needlessly hacking down Poulsen. It was a dreadful challenge by the Milan captain, and he was rightly sent off. He will have some apologising to do to his teammates, who bravely managed to get the result they needed without his help.
Howard Webb was a busy man this evening. He handed out six bookings, including the Red card that Montolivo received. It was the correct call, as Poulsen could easily have suffered a broken leg. He controlled the game remarkably well, in what was a very heated affair, and further underlined his status as one of the game's most reliable match officials.
AC Milan: The Italians return to Serie A action next Monday, where they will face Roma at the San Siro.
Ajax: Ajax face a trip to Cambuur Leeuwarden in the Eredivisie on Sunday.