The talented midfielder broke the deadlock after nine minutes when he curled a superb free-kick from the left into the top corner of the net.
Filippo Inzaghi doubled Milan lead in the 24th minute following an impressive counter attack.
Brazilian playmaker Kaka raced down the left flank and cut inside before providing a neat pass to Pirlo, who chipped the ball to Inzaghi and the Italian international sent a superb half-volley into the back of the net.
In the other Group D match, Shakhtar Donetsk secured a 2-0 victory over Scottish giants Glasgow Celtic.
Brandao opened the scoring as early as the fifth minute before Cristiano Lucarelli added the second just three minutes later.
The former Livorno striker received a cross from the left with a superb header that went into the bottom corner of the net.