First-half strikes from Claudio Marchisio, Arturo Vidal and Sebastian Giovinco, plus a second-half header from
Fabio Quagliarella were enough to see off the Norwegian champions as the Italians finally tasted victory after three successive draws.
For the hosts, Mauricio Isla came in for Stephan Lichtsteiner who was injured in their 3-1 loss to Inter at the weekend, while Alessandro Matri replaced Mirko Vucinic.
The visitors made two changes from the team who won 2-1 at Sonderjyske, with Soren Christensen and Morten Nordstrand making way for Andreas Laudrup and Nicolai Stokholm.
Juventus were thankful for a Vucinic strike nine minutes from time to spare the Serie A champion's blushes when the two teams met a fortnight ago.
However, it took them just six minutes to get on the scoresheet tonight as Isla's low cross from the right was converted by Marchisio from six yards out.
And they were two up after 23 minutes as Vidal capitalised on hesitant Nordsjaelland defending to slide in and divert the ball past Jesper Hansen.
The home side almost grabbed a third just three minutes later as Andrea Pirlo's corner was headed onto the crossbar from six yards out by Matri.
The visitors were struggling and needed a fine save from Hansen just after the half-hour mark, with the stopper tipping Marchisio's shot from the edge of the area round the post.
It was however three 10 minutes before the break as Sebastian Giovinco curled an effort from just inside the box into the bottom left-hand corner of the net.
The visitors did not manage a shot on goal during the opening 45 minutes and 20 minutes into the second half forced Gigi Buffon into action for the first time, with the Italian number one parrying Patrick Mtiliga's 25-yard effort. Juventus rounded off the win in the 75th minute through substitute Quagliarella.