The margin of victory could even have been greater, had Aaron Hunt not made a commendable gesture in turning down a penalty in the second half, telling the referee to change his mind after getting his foot caught in the ground.
By then, Bremen were already two goals to the good with Franco Di Santo and Philipp Bargfrede sealing all three points for Robin Dutt's men.
The win lifts them eight points clear of the relegation zone, and leaves Nurnberg five points in their wake.
The hosts actually started the brighter and they nearly took the lead early on when an Adam Hlousek cross found its way through to the far post, where it was cleared just before Hiroshi Kiyotake could reach it.
Bremen slowly found their way into the game and Di Santo was denied by the crossbar with their first chance of the game.
Just before the break, Hunt smashed a powerful shot against the inside of the post and Di Santo volleyed the rebound instinctively past Raphael Schafer, who did not emerge for the second half due to injury.
Nurnberg took the game to Bremen in the second half, but as they increased the pressure, they left Bargfrede with the run of the field, and his shot took a telling deflection off Javier Pinola to beat Schafer's replacement Patrick Rakovsky.
They were awarded the chance to make it three when Hunt went to ground inside the penalty are and the referee pointed to the pot.
Hunt's reaction was immediate, and he approached the referee to tell him his decision was wrong as Javier Pinola protested his innocence. The referee took his decision back and the game restarted with a drop ball.
Hlousek hit the crossbar late on, but there was no way back into the game for Nurnberg.