The Manchester City striker's first Italy goal since his Euro 2012 semi-final brace against Germany and strikes from midfielders Riccardo Montolivo and Daniele De Rossi enabled Cesare Prandelli's side to overcome the sending-off of Pablo Osvaldo early in the second half.
Italy took the lead after 33 minutes, Riccardo Montolivo finishing off a slick passing move by collecting Balotelli's flick before drilling a long-range effort past stationary Denmark keeper Stephan Andersen.
They doubled their lead four minutes later when Andrea Pirlo left Michael Silderbauer for dead before swinging in a teasing cross from the right that De Rossi nodded in from six yards.
Morten Olsen's Denmark side looked dead and buried but pulled a goal back with the last kick of the first half, William Kvist side-footing home a superb volley from a deflected Lars Jacobsen cross from the edge of the area.
The Danes were given another lifeline when Osvaldo was sent off 16 seconds into the second half after tussling with Nicolai Stokholm and lashing out with his left arm, catching the midfielder in the face in full view of referee Damir Skomina.
However, Balotelli restored his team's two-goal lead with 54 minutes gone, springing the offside trap and poking another magical Pirlo pass past the onrushing Andersen to seal the three points.
Italy now have 10 points, four clear of Bulgaria at the top of Group B. Denmark, on two points, are facing elimination in the face after only three games.
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