The visitors made a bright start to the match, coming close through Nicklas Bendtner and Christian Eriksen within the first 10 minutes.
The hosts did take the lead 15 minutes later, however, as Balotelli touched the ball onto Riccardo Montolivo, who fired home a fine strike from 25 yards.
The Danes got a goal back right on the stroke of half-time through William Kvist effort, the midfielder half-volleying a loose ball into the bottom corner.
This didn't seem to affect the hosts, however, as they extended their lead 10 minutes later when Balotelli beat the keeper to the ball, poking home from 10 yards.
Denmark couldn't take full advantage of their extra man as Italy held out for a hard-fought 3-1 win.