Mikkel Beckmann's excellent free-kick gave the hosts a shock lead five minutes into the second half, and Nordsjaelland held out for more than half an hour before Mirko Vucinic lashed in an equaliser.
Juventus pushed for a second but instead had to settle for another point as their Group E frustrations continued.
Juventus at least lived up to their favourites tag early on as they dominated the match.
Paolo De Ceglie fired wide from an angle on the left before Arturo Vidal blazed over following some neat passing on the edge of the area.
A poor clearance from Jesper Hansen handed Andrea Pirlo another opening in the eighth minute, but he sent his shot wide.
Sebastian Giovinco looked to have a great chance after fine control to bring down Pirlo's pass, but he was denied by a late tackle as he prepared to pull the trigger, and moments later Alessandro Matri volleyed wide after a corner.
The hosts' first chance came in the 17th minute when Kasper Lorentzen stung the palms of Gianluigi Buffon after bursting through the defence.
The Italy goalkeeper did better when Beckmann cut in from the right to send a left-footed shot towards goal.
Leonardo Bonucci got a strong head to Pirlo's 22nd-minute corner but sent it wide before Hansen was called on to keep out Giovinco's effort when the forward turned De Ceglie's drilled cross goalwards.
De Ceglie's ball then released Giovinco who rounded Hansen, only to miss the target from a tight angle.
There was almost a repeat at the other end, but Buffon gathered at the feet of Joshua John.
Vidal prodded wide after great work from Giovinco to find him at the far post, and Juventus' frustrations grew as Runje made a brilliant block to deny Alessandro Matri, following up after Hansen parried Giovinco's powerful shot.
Juventus threatened early in the second half with Hansen denying Matri and Giovinco, but it was Nordsjaelland who then took a surprise lead in the 50th minute as Buffon's hand was not strong enough to keep out Beckmann's free-kick on the eve of his 29th birthday.
Matri sought an immediate response, but Michael Parkhurst blocked his shot, before Runje threw himself in the way of an effort from Mauricio Isla.
Juventus were piling on the pressure, with Runje performing more heroics to block Marchisio's shot, and Hansen getting a hand to Giovinco's flick.
John had a chance to double the hosts' lead, but headed over from a good position.
That was a rare break in Juventus pressure, which resumed immediately as Parkhurst blocked another shot and Matri and Vidal fired wide.
Pirlo's curling free-kick in the 69th minute brought a fine save from Hansen before an ambitious volley from Giorgio Chiellini went over.
Juventus finally got their reward nine minutes from time when Isla crossed and Vucinic lashed in a volley from close range, leaving the goalkeeper with no chance.
The Italians were not satisfied with that and pushed for a winner.
Bonucci turned a corner narrowly over the bar, while Nicklas Bendtner could not keep his effort down from De Ceglie's excellent cross.