Thomas Mueller set them on their way early on before Mario Gomez struck twice.
Martin Harnik got two goals himself as Stuttgart threatened a fightback, but Bayern held on to seal a remarkable clean sweep of league, Champions League and cup.
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Who of Europe’s top strikers will move to England this summer?
After a dreadful start to their Bundesliga campaign, Borussia Dortmund appear to have weathered the storm after going five matches without defeat.