Johannes Geis' first professional goal in the 26th minute was enough for Furth to win for only the third time this season and edge to within nine points of the relegation play-off with four games of the season remaining.
Nurnberg hit the woodwork three times but came away with nothing to show for their efforts.
It was the 256th Franconian derby and one which lived up to the reputation of previous meetings between the two clubs, with nobody shirking the challenge.
It was surprising that it took the referee 13 minutes to show the first yellow card to Furth's Felix Klaus.
The next surprise came in the 26th minute when Geis scored his first goal of his career to put Furth ahead.
From almost 30 yards, the Furth midfielder took aim and found the top corner, leaving Raphael Schafer no chance in the Nurnberg goal.
Seven minutes later, Geis went close with another long-range effort, this time a curling free-kick which just missed the target.
Nevertheless, his goal was enough to give Furth the lead at the interval for the first time this season, although Hanno Balitsch almost prevented that when he hit the outside of the post.
Balitsch had the woodwork rattling again, twice, in the 62nd minute as the ball simply did not want to go in for Nurnberg.
Furth built the barricades successfully to hold on to only their third win of the season and one which means they live to fight another day.