Cesare Prandelli's men took a significant step on the road to Rio courtesy of goals from Riccardo Montolivo, Daniele De Rossi and their enigmatic Manchester City striker
Having withstood intense early pressure, the Azzurri stunned the visitors with two goals in the space of four minutes through Riccardo Montolivo and Daniele De Rossi, to put themselves in a commanding position with half-time looming.
However, William Kvist halved the home side's advantage with a volley before Osvaldo gave the Danes further reason for optimism by getting himself dismissed early in the second-half.
Mario Balotelli came to the Azzurri's aid, though, converting a terrific pass from the equally influential Andrea Pirlo to clinch a win that saw the Euro 2012 runners-up make it 10 points from a possible 12 so far in Group B.
Cesare Prandelli made four changes to the defence that had started in Armenia, which could perhaps explain why the hosts looked so shaky at the back inside the opening quarter. However, it was more down to the fact that the Danish midfield overran their Azzurri counterparts early on, allowing them to fully exploit Andrea Barzagli’s total inability to deal with Nicklas Bendtner in the air.
Indeed, the on-loan Juventus man really should have done better after being picked out by the marauding Lars Jacobsen inside the opening three minutes. Christian Eriksen then stung the palms of Morgan De Sanctis with a terrific drive from distance as the visitors continued to dominate. But, Italy gradually began to gain a foothold in the game and were desperately unfortunate not to open the scoring 18 minutes in, when Claudio Marchisio unleashed a sublime curling effort from the edge of the area that seemed destined for the top corner until Simon Kjaer popped up to block on the line.
Moments later, though, De Sanctis came to the Azzurri’s rescue again, somehow managing to keep out a low drive from Kvist with his knees. It was a highly unorthodox but undeniably crucial intervention from the Napoli goalkeeper, because Italy broke the deadlock with their next attack. Montolivo arrowed a ball into the bottom corner of the Danish net after latching onto a sublime lay-off from Balotelli.
Denmark were still coming to terms with that setback when Italy struck again, with Pirlo outfoxing Michael Silberbaeur on the right-hand side before crossing for De Rossi to head home.
The visitors were well and truly reeling, but they deservedly dragged themselves back into contention right on the stroke of half-time when the impressive Kvist guided a side-footed volley, from a deflected Jacobsen cross, past De Sanctis.
The Danes then sensed a famous win on Italian soil when Osvaldo stupidly got himself sent off for lashing out at Nicolai Stokholm less than 40 seconds after the interval. However, the loss of a man actually seemed to galvanise the Azzurri, and Balotelli in particular.
Indeed, the enigmatic forward played the lone forward role to great effect and got his just rewards for doing so when Pirlo picked out his well-timed run in behind the Denmark defence with a typically measured pass, allowing Balotelli to deftly flick the ball past Stephan Andersen.
There was no way back for Denmark thereafter, meaning their hopes of qualifying for the 2014 World Cup are now hanging by a thread, with just two points to their name after three games played. Italy, by contrast, are already well on the way to Rio.