Despite playing most of the match with 10-men due to captain Riccardo Montolivo’s first half sending off, the Rossoneri held on to gain the point they needed to book their place in the round of 16.
The away side wasted no time in their attempts to open the scoring as Christian Poulsen’s 6th minute header left Christian Abbiati flat footed but his effort connected with the inside of the post and stayed out.
The Dutch side continued to press forward in the 19th minute and forced Abbiati into a great save off a Davy Klaassen header.
Things took a turn for the worse for the Rossoneri in the 22nd minute when Montolivo was sent off for his late challenge on Poulsen. The Milan midfielder stomped on the Dane’s ankle forcing referee Howard Webb to send off the 28-year-old, setting up a difficult final 70 minutes for the Rossoneri.
Despite being a man down the home side were able to limit Ajax’s attacks for the remainder of the first half with Lasse Schone’s late free kick the only real chance conceded but his effort went well over the crossbar.
The second half started with Klassen sending in a dangerous cross that Abbiati failed to convincingly deal with before youngster Mattia De Sciglio sent the ball out for a corner.
Klassen was once again the danger man after some great passing from the Dutch side in the 66th minute but his driven effort was expertly kicked away by the veteran Milan goalkeeper.
The away side had a great chance to breakthrough in the 74th minute when substitute Kolbeinn Sigthorsson laid off a header for Viktor Fischer but the youngster sent his left footed effort inches wide of the goal.
Ajax had one last chance in the dying seconds of the match but Sigthorsson could not direct his effort on goal allowing Milan to book their place in the next round of the Champions League despite their struggles on the night.
Follow Adriano Boin on Twitter: @Boin44