Second-half goals from Bojan Krkic and Giampaolo Pazzini earned the Rossoneri the points with Michele Paolucci scoring a late consolation for the Tuscans, who remain rooted to the foot of the table, six points adrift of safety.
Milan needed a half to get warmed up, but they left Siena little chance in the second half with Bojan missing chances to score more than once in the first game since Alexandre Pato's transfer to Corinthians.
Pato's move back to his homeland provided Pazzini with a starting berth, but Milan's greatest threat in their first game of 2013 was their star of last year, Stephan El Shaarawy.
He had their only two chances in a dismal first half, beating two men only to find his match in Gianluca Pegolo in the 14th minute before missing the target in the 34th minute.
Bojan was sent on early in the second half to try to provide a spark, and he did that after just 10 minutes on the field.
He met Kevin Prince Boateng's cross at the near post to leave Pegolo no chance with his header from close range.
Pazzini earned a penalty in the 80th minute when he went down in the area under the challenge of Felipe and the Italy international stepped up to score from the spot, lifting the ball into the top left-hand corner.
Milan conceded in the 87th minute when Paolucci headed in Angelo's cross from six yards, and the Rossoneri spent the last few minutes camped in their own half defending their lead successfully.