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The Polish striker got his second of the game just two minutes later, firing in a Mario Gotze cross.
Robert Lewandowski thought he had Dortmund's third of the night just before half time, but he was judged to be in an offside position.
Nuremberg rarely threatened during the second half as the hosts continued to dominate possession and create the better of the chances.
Dortmund had several chances to increase their lead, but it was Lewandowski in the 88th minute that got the third, blasting the ball in from close range.
The win leaves Borussia Dortmund nine points behind league leaders Bayern Munich, while Nuremberg remain 15th.