Despite, their numerical advantage, Denmark were unable to find an equaliser and instead they fell further behind when Mario Balotelli poked home on 54 minutes.
Here, Sports Mole takes a closer look at where the game was won and lost.
On target: 6
On target: 4
Was the result fair?
Denmark created the majority of the game's chances, but Italy were more clinical in front of goal. It is as simple as that. Denmark worked very hard and equipped themselves well tactically. However, their finishing fell well below the required standard at international level and, for that reason alone, they deserved to lose.
Italy were below par for the opening 30 minutes, however when their chances came they were frightfully efficient. The Azzurri looked unusually shaky at the back and appeared to be missing the commanding presence of Gianluigi Buffon between the sticks. Going forward, their counter-attacking was superb.
Denmark were very confident in possession and they frustrated Italy for large periods. Also, Olsen's men created numerous opportunities to score, with overlapping full-back Lars Jacobsen and midfield playmaker Christian Eriksen looking particularly impressive going forward.
Sports Mole's man of the match
Andrea Pirlo was denied time and space. He was quiet for much of the game, but he still managed to produce two fine passes which led to Italy goals.
Damir Skomina got the big decision correct in sending off Osvaldo for violent conduct. Nevertheless, Nicklas Bendtner, who was booked for dissent later in the game, did not seem too impressed by the Slovenian official and Denmark may argue that he perhaps afforded Italy goalkeeper Morgan De Sanctis a little too much protection from crosses.
Italy sit proudly atop of Group B and their next competitive test is a trip to Malta in March. Before then, they take on France in a Parma friendly next month.
Denmark, who are now in desperate need of a win, face the Czech Republic and Bulgaria in a March double-header.