Azzurri coach Prandelli has tinkered with teams and formations since Italy began their qualifying campaign with a lucky 2-2 draw away to Bulgaria last month.
But after four of their 10 matches the four-time World Cup winners have 10 points from a possible 12 at the top of Group B with second-placed Bulgaria four points adrift.
Prandelli has come under scrutiny since September’s draw in Sofia and a poor performance in a 2-0 win over Malta four days later.
But the former Fiorentina handler looked relaxed as he considered a worry-free lead-up to Christmas before qualifying for Brazil 2014 resumes with a trip to Malta in March 2013.
“Our next match is in March, that’s why these three points are so important,” said Prandelli.
“In the standings, we’re in a good position but it’s early days yet. We wanted to celebrate Christmas in advance this year.”
Italy had to do without influential ‘keeper and captain Gianluigi Buffon after the Juventus star failed a late fitness test having picked up a thigh niggle in Friday’s 3-1 win over Armenia.
Napoli keeper Morgan De Sanctis stepped in, and Italy also welcomed the return of Manchester City striker Mario Balotelli who had missed their three previous qualifiers.
Despite a shaky start against the Danes, who came to Italy with only two draws to their name, Italy rode their luck to open the scoring through AC Milan midfielder Riccardo Montolivo.
Despite having Balotelli to his right, the AC Milan midfielder’s rightful decision to strike from the edge of the area saw Danish ‘keeper Stephan Andersen well beaten in the 33rd minute.
Three minutes later Andersen was beaten again when De Rossi’s glancing header from Pirlo’s superb curling cross doubled Italy’s lead.
Denmark reduced the arrears in first half injury time after Lars Jacobsen’s cross from the right deflected off the head of Italy defender Federico Balzaretti.
It dropped fortuitously in the path of Stuttgart midfielder William Kvist, who beat De Sanctis low to his right with a powerful volley from the edge of the area.
Italy were given another fright only a minute after the restart when Balotelli’s strike partner Pablo Osvaldo was sent off for using his hand to fend off the attention of defender Nicolai Stokholm.
If the 37,000 crowd at the San Siro thought Italy would crumble, their fears were allayed in spectacular fashion when Balotelli beat an advancing Andersen to Andrea Pirlo’s long midfield ball to poke the ball into the net on 54 minutes.
Denmark coach Morten Olsen, whose side have yet to win in three games, said Italy’s loss of Osvaldo had changed little.
“We know that Italy are famous for their ten-man defence, it didn’t change much for us having a man advantage,” said Olsen.
Despite holding olny two points from three games, he added: “I believe we played well. I didn’t believe we’d bring back three points from Italy.
“The points we lost, we lost them (in a draw) against the Czech Republic.”
Prandelli, meanwhile, hinted that his side could finally be getting close to the level they possessed on their way to an unlikely final place at the Euro earlier this year.
“I’m happy because we showed a lot of commitment out there, and I liked that,” added the Italian.
“We still have a lot to improve on and things have been complicated in the last few days but the boys have been very professional and their commitment tonight pleased me a lot.”