BERLIN — Mario Gomez scored twice as Bayern Munich beat Nuremberg 4-0 in the 183rd Bavarian derby to open a four-point lead in the Bundesliga on Saturday, with defending champion Borussia Dortmund held 1-1 at Stuttgart. Gomez scored in the second minute and rounded off the scoring in the 68th, following goals from Bastian Schweinsteiger and Franck Ribery in the 19th and 39th. “When we play like this we’re unstoppable,” Gomez said. Serdar Tasci scored in the 22nd for Stuttgart, but Lukasz Piszczek equalized in first-half injury time. Schalke beat Hoffenheim 3-1 to climb to second, one point ahead of Dortmund. Hertha Berlin won 3-2 at Wolfsburg and Borussia Moenchengladbach beat Hannover 2-1. In the late game, Werder Bremen came from behind to win 3-1 at Mainz to move fourth behind Dortmund on goal difference. Niko Bungert headed Mainz in front in the 23rd, but the outstanding Claudio Pizarro went past four Mainz defenders before putting the ball over Christian Wetklo for his 150th Bundesliga goal six minutes later. “It’s my job,” Pizarro said. The Peru striker also set up Aaron Hunt to score with an impressive long-range strike 62 seconds after the interval. Sebastian Proedl crashed a header off the post in the 78th, but made the game safe when he scored at the second attempt. “I’ve no more desire to talk about the good game my team played,” said Mainz coach Thomas Tuchel after his side’s fifth home defeat in a row. “I’ve been saying the same stuff for the last nine weeks.” Bayern — which hosts Napoli in the Champions League on Wednesday — got off to a perfect start when Gomez scored with a powerful header from Schweinsteiger’s precise cross. The league’s top scorer returned the favor for Schweinsteiger to score from distance, 20 minutes before Ribery unleashed a low strike past the helpless Alexander Stephan. Bayern’s intensity dropped in the second half, when Nuremberg’s Tomas Pekhart should have scored only to be let down by his first touch. But any lingering hopes of an unlikely comeback were dashed when Toni Kroos crossed for Gomez to score his 12th goal of the season from close range. “We could have gone forward more often in the second half,” Gomez said. “A lot of the players were already thinking of Wednesday’s game. The fans have to excuse us if we don’t go forward so aggressively once it’s 3-0 or 4-0, because we have to think of the coming weeks.” It was Bayern coach Jupp Heynckes’ first win over a side coached by his counterpart Dieter Hecking at the fifth attempt. “You can see the players are enjoying themselves playing soccer. It’s a very important aspect of playing successful soccer,” Heynckes said. Kickoff in Stuttgart began 15 minutes later after the visitors were delayed in traffic. Robert Lewandowski hit the post for Dortmund in the third, when Mario Goetze also shot narrowly wide. Tasci was first to react when Martin Harnik’s effort struck the post and the defender slid in to score off the rebound. Goetze was unlucky not to get a penalty in the 37th, when the 19-year-old was upended by Christian Molinaro.