Alberto Gilardino and Clarence Seedorf scored two goals apiece to give Milan a comfortable win. Cristiano Lucarelli scored the consolation for Shakhtar.

The Rossoneri, who were handed a stunning 1-0 defeat by Empoli in the Serie A, are on top of Group D with six points, level with second-placed Shakhtar who have an inferior goal difference.

Portugal's Benfica, who beat Celtic 1-0, come third on three points while the Scottish giants are fourth with same amount.

Gilardino, who broke his duck in Milan's 5-1 drubbing of Lazio earlier this month, opened the scoring after six minutes when he rose at the near post to head Andrea Pirlo's corner into the far corner.

He stretched the lead eight minutes later in a similar fashion, heading home Seedorf's pinpoint cross from the left.

Former Livorno striker Cristiano Lucarelli pulled one back for Shakhtar six minutes after the interval following a dreadful error by Massimo Oddo.

The right-back gave the ball away inside the area to Brandao, whose initial shot was blocked by keeper Zeljko Kalac into the path of Lucarelli, who notched home.

Seedorf killed off the visitors' hopes in the 62nd minute when he brilliantly controlled Pirlo's corner on his left foot before sending a superb volley into the bottom corner of the net.

He completed the rout seven minutes later through another superb long-range volley after spotting Shakhtar keeper Andriy Pyatov off his goal.