Both sides were without some key players as they played out an entertaining match.
Robinho put Milan ahead, before goals from Claudio Marchisio and Arturo Vidal gave the champions the edge.
Alessandro Matri put Juve 3-1 ahead before Robinho pulled one back with a penalty.
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The reputation of the Premier League means it is the most popular and one of the most watched leagues in the world.
Five English clubs will compete in the last sixteen of the Champions League for the first time ever as Liverpool, Manchester United, Manchester City, Chelsea and Tottenham face some difficult away matches.