Hiroshi Kiyotake put the visitors ahead in the 21st minute and, although Tobias Werner equalised before half-time, Alexander Esswein restored Nuremberg's lead soon after the break.
The result saw Nuremberg a 10-point advantage over the third-bottom hosts.
Having picked up 12 points since the turn of the year, Augsburg came into the game in confident mood, seeking to reduce the arrears on their opponents to just four points.
What they had not counted on, though, was a well-organised Nuremberg side who resisted their assaults before going in front with one of their first attacks.
Esswein was put through by Tomas Pekhart and he lifted the ball back to Kiyotake, who did not need to be asked twice and volleyed home from 15 yards.
It was a slap in the face for Augsburg, who had dominated the game until then, albeit without creating any clear-cut chances.
They then followed Nuremberg's lead by converting their first big chance of the game to level in the 36th minute.
Werner's header should have been easy pickings for Raphael Schafer, and it looked every bit like the Nuremberg goalkeeper had denied the Augsburg striker, but somehow the ball slipped out of his grasp and through his legs, into his own goal.
Nuremberg stuck to their guns and continued to wait for chances on the counter-attack.
They took the lead for the second time in the 54th minute when Esswein's low free-kick from just outside the penalty area found its way in.
Augsburg inevitably pushed forward in search of an equaliser, but Nuremberg were always a threat on the break.
Five minutes from time, substitute Tolga Danabli headed against the post, but it was not a costly miss as Nuremberg held on to take all three points and move up to 11th in the table.