Italy got the convincing win they needed to silence some of their critics despite playing virtually the entire second half with 10 men at home to Denmark.
Two goals in the space of five first-half minutes from Riccardo Montolivo and Daniele De Rossi had them 2-0 up eight minutes before the break, although Denmark got a goal back in first-half injury time through William Kvist Jorgensen.
Then, just 18 seconds into the second half, Italy's Pablo Osvaldo was shown red for violent conduct after an incident involving Denmark's Nicolai Stokholm.
However, Cesare Prandelli's team, largely unimpressive in their World Cup qualifying campaign so far, did not let that throw them off their stride as Mario Balotelli - making his first appearance for Italy since Euro 2012 - fired in a third in the 54th minute.
The mercurial Balotelli's first contribution had been to concede a free-kick as Denmark mounted an early attack but after Nicklas Bendtner fired wide, Italy began to find their feet.
Montolivo tried a sighter from a long range before Stokholm blocked Osvaldo's shot to concede a corner.
Morgan De Sanctis, starting in goal in place of the injured Gianluigi Buffon for Italy, was called on to tip Christian Eriksen's 30-yard shot over the crossbar.
Osvaldo headed wide from Ignazio Abate's cross before Simon Kjaer got in a block to concede a corner when Federico Balzaretti drilled an effort from outside the area.
Denmark threatened again just after the half-hour mark, with Kvist Jorgensen's shot tipped over by De Sanctis before Bendtner headed over from the resulting corner.
But moments later it was Italy who led with Balotelli reminding Italy why they had missed him, the Manchester City striker picking out Montolivo to lash the ball home.
Denmark had barely recovered from that when it became two with Andrea Pirlo crossing for De Rossi to head in from close range.
Denmark twice threatened in quick succession with Lars Jacobsen shooting over and Dennis Rommedahl sending an effort narrowly wide before they got their goal, Kvist Jorgensen finishing from the edge of the area after being picked out by Jacobsen.
Given their recent shaky form, Osvaldo's red card might have rattled Italy when it came so soon in the second half, but instead they pulled further clear, with Pirlo teeing up Balotelli to fire a shot low into the net.
Denmark pushed for a way back into the game, but Michael Krohn-Delhi curled a shot over and Daniel Agger's more powerful effort was likewise too high.
Eriksen joined in with another shot from range that drifted over the crossbar and the chances began to dry up with Italy looking to consolidate their position.
Understandably, there was little ambition shown by the outnumbered Italians, but they almost nicked a fourth when Stephan Andersen fumbled Montolivo's long-range effort inside the final 10 minutes.
The win sees Italy move four points clear of Bulgaria at the top of Group B although third-placed Czech Republic, five points back, have a game in hand.
Denmark are in trouble with only two points from three matches.