The Danes stunned the Bianconeri by taking the lead shortly after the interval with a sublime set piece and then, after Mirko Vucinic's equalizer, somehow held on for a point.
However, it could have been even worse for the Bianconeri, who fell behind to a stunning free kick goal from Mikkel Beckmann early in the second half. Indeed, there were just under 10 minutes remaining when the Italian champion finally drew level through substitute Mirko Vucinic.
Fellow replacement Nicklas Bendtner had a chance to be a hero on home soil but he headed wide late on and Juve was forced to settle for its third successive draw in this season's Champions League - and ninth in total in European competition.
The Bianconeri had gone into the game in Copenhagen knowing that nothing less than a victory would suffice if the club was to retain any real chance of progressing as winner of Group E - or perhaps even progressing at all.
Still, while the visitors, and Andrea Pirlo in particular, were undoubtedly intent on taking control of the game early on, FCN was in no mood to be pushed around and enjoyed plenty of possession in the opening exchanges.
Indeed, with Kasper Lorentzen, Joshua John and Andreas Laudrup all impressing in support of lone frontman Beckmann, the tournament debutant carried an undeniable attacking threat. The club could even have taken the lead on the half hour when John latched onto a kick from Jesper Hansen and looked to flick the ball past the onrushing Gianluigi Buffon only to see the goalkeeper rather fortuitously block with the side of his chest when it could so easily have been his flailing left arm.
However, it was Juve, with Pirlo predictably pulling the strings, which looked the more likely to score in a tight opening 45 minutes. With one superbly-executed, first-time pass in behind the FCN defense, Pirlo put Sebastian Giovinco in on goal only for the diminutive forward to be muscled off the ball by the impressive Jores Okore.
It was undoubtedly Giovinco who was carrying the Bianconeri’s most potent attacking threat but after seeing a smart volley saved by Jesper Hansen on 28 minutes, the former Parma man squandered a terrific chance to break the deadlock moments later after being played through by Paolo De Ceglie. Giovinco rounded the advancing Hansen with ease but allowed the acute angle to get the better of him and fired into the side netting.
The diminutive forward also tested Hansen with stinging drives either side of half time, first after sending the scrambling FCN defence one way and then the other, and then after latching onto a fine knock-on by strike partner Alessandro Matri.
The opening goal, therefore, came as a real bolt from the blue - and Juventus only had itself to blame, some sloppy play in midfield eventually leading to De Ceglie putting his own defense under pressure with a poor pass before an unsettled Giorgio Chiellini needlessly barged Laudrup out of the way on the edge of the area.
Beckmann, whose shooting up until this point had been tame at best, stepped up to take the resulting free kick and calmly curled the ball up and over the wall and into the top right corner, sparking raucous celebrations from the home side's supporters.
Juventus, unsurprisingly, redoubled its efforts in a bid to drag back into the game and Giovinco, after rising wonderfully to meet another fine De Ceglie delivery, was only denied a long overdue goal by the most amazing one-handed save from Hansen.
The Italian champion continued to press, sending Bendtner and Vucinic on to bolster its attacking ranks. In the end, it was the latter who made the breakthrough, volleying home a fine cross from Mauricio Isla from wide on the right side with just under 10 minutes remaining.
Bendtner, though, could have really kick started his Juventus career on 87 minutes but he headed another inviting cross from De Ceglie well wide after arriving late into the area. In truth, though, it was probably only just that FCN held on to claim the greatest result in the club's 21-year history.
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