Despite an encouraging start from the newly-promoted hosts, Bayern's class and experience eventually got the better of them.
Bayern had the lion's share of the possession for most of the first half but failed to make any concrete attempt on goal until the 43rd minute.
With Greuther holding on for a goalless scoreline at the break, Thomas Muller found the target for the Bavarian giants from close range after a deflected cross kindly fell to his feet.
Mike Buskens's side tried to make a strong comeback in the second half, but Xherdan Shaqiri's quashed their hopes of an equaliser.
The Switzerland international was the architect of Bayern's second goal on the hour mark, as he released Arjen Robben down the right. Robben's attempt was parried by Max Grun but the ball was then slotted home from close range by Mario Mandzukic.
Bayern continued to dominate proceedings for the remainder of the game at the Trolli Arena in Furth, and added to their tally in the 79th minute when Robben's cross took a huge deflection off Thomas Kleine and found its way into the Greuther goal.