The Italian side needed to win by four points to progress from Group C at the expense of their hosts and they did so after a thrilling final few minutes.
Down by 11 points in the third period, Milano staged an astonishing final-quarter comeback to win by six points - more than what was required to edge out their opponents.
Both teams finished the regular season with records of 4-5 and were tied for fourth place. But tiebreakers gave Milano the edge and it is they who progress to the Top 16.
Partizan failed to qualify for the first time in six seasons.
Fenerbahce Ulker claimed top spot in Group A with an 83-76 away win over Cantu that saw them improve their record to 6-4. The Italian side ended with five wins and five losses to progress in third place.
Also finishing with records of 5-5 were Bilbao Basket and Caja Laboral after Bilbao won an all-Spanish clash 77-72 at home. But the tiebreakers meant Caja finished in fifth, missing out on the Top 16, while Bilbao progressed in fourth.
Olympiacos came second in Group A after a 79-74 win over Nancy in France saw them finish with a record of 6-4 - level with Fenerbahce. But the Turkish champions claimed top spot thanks to the tiebreaker.
Real Madrid topped Group C after beating Efes Pilsen 75-66 while Maccabi Tel Aviv sealed second place after an 86-69 win at Spirou Basket Charleroi.