The Swiss striker rose from the bench to clinch the victory three minutes from time, with Lucien Favre's men squandering the chance to overtake Bayern Munich in second
After a tight affair, Albert Bunjaku rose from the bench to give his side an unlikely victory after a drab match characterised by sloppy play and missed chances.
The encounter commenced with both sides seeming eager to notch an early strike. Markus Feulner was unable to capitalise on some good work from his Nurnberg team-mate, lashing an effort high and wide.
At the other end, Marco Reus made an early drive down the right, but his disappointing delivery was lapped up by the hosts' defensive ranks.
Raphael Schafer was called into action twice in quick succession. Igor De Camargo fed Reus, whose first-time shot was beaten away by the Nurnberg skipper, before a swerving effort from Mike Hanke was impressively beaten away.
At the other end, Timothy Chandler crossed to Alexander Esswein, who contrived to miscue an effort from inside the area, sending the ball into touch when he could have put his side ahead.
However, as the match wore on, chances became few and far between as both defences dropped back. The best chance of the first half came minutes from the break. Ter Stegen claimed a tame header from Dominic Maroh, and immediately sent the ball up-field to Reus.
The Dortmund-bound forward played in Havard Nordtveit, but in his eagerness to check back onto his favoured right foot, the Norwegian was dispossessed when he should have shot.
Seconds after the restart, Arango should have put his side ahead. A Hanke cross was comically missed missed by Chandler, but as the ball fell to the Venezuelan, Schafer was quick off his line to claim the ball.
The hosts continued to press for the opener as the game wore on. An Adam Hlousek set-piece dropped to Philipp Wollscheid, who, amid appeals for a penalty, prodded the ball disappointingly wide.
With the final quarter of an hour looming, Maroh was inches away from putting his side ahead as he stretched to reach a Hlousek set-piece at the far post, only to see the ball drift past him.
Ter Stegen was called into action, dropping low to save a Markus Feulner effort at the near post, before Christian Eigler appealed for a penalty against Nordtveit, after his cross struck the former Arsenal man's arm.
A frustrated Hanke failed to prod Arango's ranging pass into Oscar Wendt's path, before Nurnberg finally dealt the killer blow.
Esswein motored down the left, leaving Martin Stranzl in his wake, and crossed to Bunjaku, who drove the ball past Ter Stegen with just three minutes remaining to clinch the victory.
Borussia Monchengladbach remain in third, a point behind Bayern Munich, while Nurnberg look certain to avoid the drop, having opened up a nine-point gap between themselves and Augsburg.