With Bayern at south German rivals VfB Stuttgart on Sunday, Dortmund took their opportunity to move up to second ahead of Bayer Leverkusen, who are at Freiburg on Saturday night.
There was a strong Poland theme to Dortmund's scoresheet with national team-mates, midfielder Jakub Blaszczykowski, who netted a controversial first-half penalty, and striker Robert Lewandowski, sharing the goals.
"Nuremberg actually had the better chances, although we had 80 percent possession," admitted Dortmund coach Jürgen Klopp after a match played in sub-zero temperatures.
"If our goalkeeper hadn't made two sensational saves, Nuremberg would have taken an early lead. We had to be patient, which was the test we passed, and at the end of the day, winning 3-0 is a good thing."
Nuremberg last scored a goal in Dortmund back in 2006 and this was their 14th visit to Borussia without a win.
"The first-half penalty they were awarded was definitely questionable and at the end, the result was probably a goal too many," said Nuremberg coach Michael Wiesinger.
"The second half was a brave performance from us. It is a bitter defeat, but they do not give us much to work with."
Nuremberg's Czech republic striker Tomas Pekhart, then midfielder Markus Feulner forced Borussia goalkeeper Roman Weidenfeller into reflex saves with 15 minutes gone, but Dortmund raced into a 2-0 lead soon after.
Poland captain Blaszczykowski - known as Kuba - scored twice in three minutes during a devastating first-half spell.
After Nuremberg winger Timo Gebhart was judged to have fouled Dortmund right-back Lukasz Piszczek, Kuba drilled home the penalty on 18th minutes and then slotted his second after Germany star Mario Götze's cross found him.
Dortmund were rarely threatened in the second half, as midfielder Nuri Sahin came on to make his first appearance at home since his return from 18 months away at Real Madrid and Liverpool.
With two minutes left, Germany midfielder Marco Reus set up Lewandowski, who blasted home his 12th league goal of the season to make sure of the points.