Milan move two points behind fourth-placed Fiorentina - held 2-2 by Sampdoria - thanks to a Filippo Inzaghi hat-trick.
Livorno 1-4 AC Milan
AC Milan won 4-1 at Livorno a result which boosts the Rossoneri's Champions League hopes as it brings them to within two points of 4th placed Fiorentina.
Filippo Inzaghi opened the scoring in the 23rd minute, scored his second seven minutes into the second half and completed his treble seven minutes later.
Clarence Seedorf added a fourth in the 70th minute before Dario Knezevic pulled a goal back for the home side two minutes later.
Fiorentina 2-2 Sampdoria
Fiorentina trailed to Christian Maggio's 63rd-minute goal but must have thought they had beaten Samp when Christian Vieri levelled in the 77th minute and Adrian Mutu converted an 84th-minute penalty.
But Daniele Gastaldello's stoppage-time equaliser earned a point for the visitors.
Fiorentina looked a little tired, as they are still battling in the UEFA Cup and can claim a place in the UEFA Cup final if they beat Glasgow Rangers on Thursday.