Bayern continued to dominate and took the lead in the 23rd minute through Schweinsteiger, who rose unmarked to head home from Arjen Robben's corner.
The Bavarians were in complete control and scored a second nine minutes later. Robben laid the ball off for Toni Kroos on the edge of the box and the midfielder placed a low effort into the bottom corner past Tobias Sippel.
Five minutes into the second half Muller scored Bayern's third goal of the evening from the penalty spot after Robben had been brought down inside the box.
They should have added a fourth moments later, but Franck Ribery blazed a strike over the bar after being picked out at the back post by Robben.
Mandzukic should have grabbed his second of the game soon after, but headed Gotze's cross wide just wide of the far post.
In the final minute Gotze scored a fifth for Bayern after latching on to Robben's backheel and calmly slotting home from close range.