In the 255th meeting between the clubs, Markus Feulner was sent off for Nuremberg in the 35th minute while Sercan Sararer also saw red after picking up his second booking for Furth after 61 minutes.
Furth remain winless in 11 matches, while the draw ensured Nuremberg have been beaten just once in four matches.
Neither team created many chances in the first half hour of a hard-fought clash between two struggling clubs.
Furth had the first opportunity in the 34th minute after a blunder by Nuremberg defender Javier Pinola although Gerald Asamoah could not beat keeper Raphael Schafer one-on-one and Timm Klose was able to clear the ball.
Nuremberg were a man down a minute later as Feulner was shown red for his rash challenge on Stephan Furstner right in front of referee Felix Brych.
The sides were evened up in the 61st minute as Sararer received his second warning for a foul on Pinola, who then made a fine last-gasp interception on Edgar Prib.
Neither team was able to push forward much thereafter.