Gladbach came quickly out of the blocks and could have gone ahead inside three minutes, but Patrick Herrmann's shot from inside the box was directed straight at Raphael Schafer in the home goal.
The hosts started to come into the game after Gladbach's strong start and it was Adam Hlousek's turn to shoot, but he too made his effort comfortable for the goalkeeper with Marc-Andre ter Stegen making the save.
It was Gladbach who opened the scoring in an even game to that point, as Juan Arango's free kick from deep on the left took a huge deflection and found its way past Schafer.
Nuremberg were the better team for the rest of the half and were very unlucky not to level matters on 35 minutes, as Josip Drmic saw his header from a Hiroshi Kiyotake cross cannon back off the bar.
With the home side needing to score, Gladbach were able to remain patient and they wrapped up the win with 10 minutes to spare as Max Kruse converted a penalty after Mike Frantz had brought him down.