Five-star Bayern beat Dortmund, Cologne sink Schalke
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The Polish hot-shot netted Bayern's third and fourth goals at Munich's Allianz Arena after Germany forward Thomas Muller's double, including a first-half penalty. Mario Gotze grabbed Bayern's fifth to compound his former club's misery.
Earlier, third-placed Schalke crashed to their first defeat in seven games with a 3-0 loss at home to Cologne, who took their chance to climb to fifth. Cologne's French striker Anthony Modeste claimed his sixth goal in eight matches before the visitors ran riot in the final ten minutes.
Cologne doubled their lead at Gelsenkirchen's Veltins Arena when defensive midfielder Yannick Gerhardt netted on 79 minutes, before Simon Voller drilled home a shot, just a minute after coming on, on 84 minutes.
Bayer Leverkusen and Augsburg battled to a 1-1 draw.