Bosnia international Vedad Ibisevic converted a third-minute penalty before Nuremberg levelled three minutes later through Josip Drmic following a fine through ball from Timothy Chandler.
Stuttgart, who have gone seven games without defeat since Schneider took over from Bruno Labbadia, were the better side.
They hit the post through Ibrahima Traore while Austrian Martin Harnik also missed two golden chances for the hosts in the first half.
Nuremberg, with Dutch coach Gertjan Verbeek in charge for the first time, came agonisingly close when Daniel Ginczek fired wide from close range.
Stuttgart have 13 points from 10 games, 10 behind leaders Bayern Munich, while third from bottom Nuremberg are on seven points.
Bayern entertain promoted Hertha Berlin on Saturday while second-placed Borussia Dortmund, a point behind, travel to bitter rivals Schalke 04 for the 83rd Ruhr Valley derby.