The game at the San Siro Stadium ended 2-1 in favor of Stefano Pioli's team.
As part of Milan, the ball was scored by Theo Hernandez (21-minute), Olivier Giroud (89th).
At Spezia, Daniel Maldini scored (59th).
Giroud immediately after the goal received a second yellow card and left the field.
Milan are second in the standings with 29 points.
Spezia are in 17th position with nine points.
Earlier it was reported that Napoli defeated Atalanta away in the match of the 13th round of the Italian Football Championship.