The win moved Milan closer to the zero point as they start the season on minus eight for their role in the sporting fraud scandal that hit the Italian League last season.

Lazio, also involved in the same case, remain -11 after the defeat.

Italy striker Filippo Inzaghi put Milan ahead in the 27th minute when he struck home from the edge of the area after being set up by Kaka.

Oliviera, in for Alberto Gilardino, headed an Andrea Pirlo corner-kick home in the 70th minute to double the lead.

Three minutes later, Nigerian Stephen Makinwa pulled one back for Lazio as he converted a low cross home from close range.

Oliviera almost scored again after dancing his way past three defenders but his shot was blocked by Lazio keeper Angelo Peruzzi.

In another match, Atalanta grabbed the league summit with a 3-1 win over Ascoli.

Former Inter Milan forward Nicola Ventola posted a brace and Riccardo Zampagna added the third in the net of veteran keeper Gianluca Pagliuca, who tied Dino Zoff's record of 570 games in the league.

Sasa Bjelanovic headed home to score the consolation goal for Ascoli.