Leaders Bayern Munich extended both their unbeaten Bundesliga records with a 2-0 win at Nuremberg on Saturday while third-placed Borussia Dortmund romped to a 5-1 win in Bremen.

European champions Bayern remained 13 points clear in the Bundesliga as the runaway leaders left Nuremberg with 56 out of a possible 60 points this season.

This was Bayern's 45th unbeaten Bundesliga match, dating back to October 2012, and their 29th unbeaten away league game to extend their records with a rare win in Nuremberg.

"I quickly noticed why Bayern had only won once in six years at Nuremberg," said Bayern coach Pep 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."

Despite the heavy 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," admitted Nuremberg coach Gertjan Verbeek.

"It was almost impossible to come back after they went 2-0 up soon after the break."

Bayern needed just 17 minutes to take the lead at Nuremberg's Grundig Stadium when Germany star Mario Goetze put David Alaba in space down the flank and the Austria left-back flicked in a cross for Mario Mandzukic to volley home.

The Croatia striker then turned provider when he put captain Philipp Lahm in space to fire home on 49 minutes as Bayern counter-attacked.

It should have been more when Arjen Robben hit the post ten minutes later, but Bayern were in complete control.

Dortmund dismantled Werder 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."

Dortmund made their pressing game count when defender Marcel Schmelzer pounced on a mistake on the left and slid his pass in for Lewandowski to hit the top right-hand corner with 26 minutes gone.

Dortmund doubled the lead at Bremen's Weser Stadion when Armenia's Mkhitaryan scored his first league goal since September as he blasted his shot into the left-hand corner four minutes from the break.

Veteran centre-back Manuel Friedrich then volleyed home just after the interval to claim his first Bundesliga goal for two years.

Lukasz Piszczek's shot clipped the crossbar on 56 minutes, but Dortmund grabbed their fourth when Mkhitaryan curled in his second after Marco Reus's superb back-heel pass on 62 minutes before Lewandowski added a late fifth.

Bremen midfielder Levent Aycicek scored a late consolation on his Bundesliga debut, but there was precious little else for Werder fans to enjoy.

This was the 12th time this season Bremen have conceded three or more goals and coach Robin Dutt is under increasing pressure with his side 13th and just three points from the relegation places.

Hamburg coach Bert van Marwijk is coming under increasing pressure as his side slumped to their sixth straight defeat, losing 3-0 at home to Hertha Berlin.

Colombia striker Adrian Ramos, who has been linked to Real Madrid and Borussia Dortmund for next season, scored twice to leave Hamburg second from bottom as they were booed by their own fans after the final whistle.

In the basement battle, Eintracht Frankfurt moved up to 12th with a 3-0 win at home to bottom side Eintracht Braunschweig.

Freiburg were held to a 1-1 draw at home to Hoffenheim while sixth-placed VfL Wolfsburg enjoyed a 3-0 win at home to Mainz 05.

On Friday, second-placed Bayer Leverkusen enjoyed a 1-0 win at Borussia Moenchengladbach with South Korea's Son Heung-Min scoring the second-half winner.