A rare goal by the unlikely Thomas Helveg handed Deportivo La Coruna their first Champions League defeat of the season.
AC Milan will celebrate all the way back to Italy after they threw away a win against Galatasary two weeks ago and the ten week break in European action can now only help to strengthen the Milan squad as the Italian transfer season opens next week.
Milan did a typically well organised job of defending against the free flowing Liga leaders and limited the chances for the home team to score.
Deportivo were well on top for most of the first half but Helveg pushed on with a run in first half injury time and drove the ball into the net to give Milan the goal they could defend.
Earlier Djalminha had run clear of the Milan defence on the half hour mark to send in a low cross shot but Roque Junior managed to scramble it away from the goal line.
Deportivo dominated the second half but Milan were able to use the runs of Andriy Shevchenko to relieve pressure on their disciplined defence and they held out for the win as the Liga side failed to create a clear cut chance to score.
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