Vedad Ibisevic gave the visitors the lead with the quickest goal in the Bundesliga this season inside the opening minute before Martin Harnik wrapped up the win in the 75th minute.
Stuttgart's players celebrated with their coach after claiming their first win of the season while consigning Nuremberg to a third successive defeat.
The pressure was mounting on Labbadia following the team's poor start to the campaign, but that was lifted a little in the very first minute when Ibisevic put the Swabians in front.
It was a gift for the Bosnian striker with Marcos Antonio playing a poor pass back to his goalkeeper and Ibisevic pounced to accept the gift as many of the fans inside the Frankenstadion were still taking their seats, placing his shot in from 10 yards with Raphael Schafer off his line after just 24 seconds.
Having settled down, the fans then saw Nuremberg seemingly draw level, only for the effort to be ruled out. Marcos Antonio headed the ball forward and Timm Klose turned it in from close range, but the linesman's flag cut short the celebrations.
Nuremberg, whose own coach Dieter Hecking will now have plenty of questions to answer, tried to respond, but struggled to create any serious moments of danger.
Stuttgart then cleverly struck on the break to make it 2-0 and wrap up victory.
Ibisevic was the provider for Harnik 15 minutes from time the Austria international threading his shot inside the near post, sparking celebrations on the touchline.