The Bavarian giants started by passing the ball around in typical fashion, but they did not have an effort until the 10th minute, when Toni Kroos shot from distance but it was kept out by Jaroslav Drobny.
Hakan Calhanoglu decided to have an effort from distance himself five minutes later, but the Turkish international's shot was held by Manuel Neuer.
Both sides continued to struggle to create chances and Milan Badelj summed up the first half with a wayward shot from outside the box.
However, just before the break Mandzukic met a Rafinha cross to head his side in front from close range.
Not long after the restart Bayern had the second goal that they deserved, as Gotze cut in after a fine touch and finished into the bottom corner.