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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Summer 2016 is set to be a very exciting time for football fans, as this is when the long awaited Euro 2016 tournament kicks off.
Since Guus Hiddink arrived at the helm, Chelsea have improved considerably after a tricky start to the campaign.