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.
CZECH REPUBLIC 0-0 BULGARIA
The Czech Republic and Bulgaria drew 0-0 in a World Cup Group B qualifier in a match in which the home side appeared to lack any attacking urgency until the final minutes in Prague.
The hosts, who beat Malta 3-1 on Friday, controlled much of the early possession and went close to taking the lead in the 40th minute when Petr Jiracek directed a header wide with only the keeper to beat.
Bulgaria started the second half brightly but the Czechs regrouped and had a glorious chance when Bulgarian keeper Nikolay Mihaylov bungled Jaroslav Plasil's long cross, only for a defender to clear away Tomas Sivok's header on goal.
Czech coach Michal Bilek threw on attacking players Vladimir Darida, David Lafata and Marek Vydra in the second half but the home side could not penetrate the Bulgarian back line.
The Czechs have five points from three games and Bulgaria six from four matches.