Hansi Flick's men should have doubled their advantage at the hour mark but Philippe Coutinho's well-placed curl got denied by the crossbar.
Schalke responded out of the blue and almost caught the visitors flat footed but substitute Benito Raman was unable to overcome Bayern custodian Manuel Neuer following a promising fast break.
The hosts threw everything up front but Bayern held firm and extended their unbeaten run against Schalke to 21 games in a row.
"My team played very well and I am satisfied with the performance but Bayern is the deserved winner of the game," Schalke coach David Wagner said.
"We are of course delighted with the outcome of the game. Schalke played defensively but we played it smart and booked our berth for the next round," Bayern coach Hansi Flick said.
Elsewhere, fourth division outfit Saarbrucken flabbergasted top flight team Fortuna Dusseldorf 7-6 (1-1) in the penalty shootout. With the result, Saarbrucken is the first-ever fourth division club that advance into the semifinals.
The following fixtures conclude the quarterfinals on Wednesday - Bayer Leverkusen host Union Berlin and Eintracht Frankfurt clash with Werder Bremen.
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