European champions Bayern remained 13 points clear in the Bundesliga as goals by Mario Mandzukic and captain Philipp Lahm sealed the Bavarian giants' 2-0 win with 56 out of a possible 60 points this season.
It was Bayern's 45th unbeaten Bundesliga match, dating back to October 2012, and their 29th unbeaten away league game to extend their records after a rare win in Nuremberg on Saturday.
But Bayern did not have things all their own way leaving coach Pep Guardiola to criticize the pitch at the Grundig Stadium which hampered Munich's dominant passing game.
"I quickly noticed why Bayern had only won once in six years at Nuremberg," said Guardiola.
"Nuremberg were aggressive and played very intensively, they had two or three clear chances.
"After we went 2-0 up, things got easier for us, but the pitch made things difficult and wasn't good for our possession and short passing game.
"That is why we tried to put in more long balls, but our attitude was incredible."
Despite the surface, Bayern still enjoyed more than 60 percent possession - down from the average of 75 they are accustomed to - while defeat dropped Nuremberg back into the bottom three.
"The first-half cost us a lot of strength and the belief wasn't as great there after," admitted Nuremberg coach Gertjan Verbeek.
"It was almost impossible to come back after they went 2-0 up soon after the break."
Bayer Leverkusen enjoyed a 1-0 win at Borussia Mönchengladbach on Friday to stay second, while Dortmund, in third, dismantled Bremen with Poland striker Robert Lewandowski and attacking midfielder Henrikh Mkhitaryan both scoring twice.
"That was what we want to see every week and, hopefully, we will see again," said Dortmund coach Jurgen Klopp.
"We were strong as a bear in our pressing and there is very little to complain about."
Having taken just four points in five games before the winter break, Dortmund finally produced the sort of attacking football which carried them to last season's Champions League final.
"The game was huge fun to play in, and if we have fun, then results like that come around," said midfielder Nuri Sahin.
"This big victory is extremely important to us.
"We needed to finally not be nervous and played really confidently.
"This is good for our self-confidence, especially with the tough weeks coming up."
Bayern and Dortmund are in German Cup quarter-final action in midweek with Guardiola's side at Hamburg, who suffered a club record sixth straight defeat at home to Hertha Berlin on Saturday.
Dortmund are at Eintracht Frankfurt on Tuesday looking to book their place in the semi-finals having won the title in 2012.