Bayern, bidding to become the first team to win three successive editions of the competition, which was incepted in 1935, fielded a formidable starting XI at home to Eintracht Braunschweig.
David Alaba's free-kick on the stroke of half-time broke the deadlock for Pep Guardiola's men, before Mario Gotze completed a comfortable 2-0 victory
Bremen dominated the opening half-hour on their travels, but Manuel Junglas tapped home after a delightful team move to send Bielefeld in ahead at the break.
Sebastian Schuppan doubled the hosts' lead following a corner, shortly into the second half, and although Clemens Fritz's pile driver halved the deficit, Junglas' second goal of the game made it 3-1 after 83 minutes.
Bremen's misery was compounded when Fritz was sent off for a second bookable offence late on.
It was Bielefeld's second successive elimination of Bundesliga opposition, after they sunk Hertha Berlin in the previous round.
Monchengladbach had no such trouble against fourth-flight adversaries, though it took an inexplicable handball from Kickers Offenbach's Markus Muller inside his own box to enable them to go ahead.
Max Kruse converted the resulting penalty, and Patrick Herman sealed a 2-0 win.
RB Leipzig took the game to Wolfsburg, who are second in the Bundesliga, and Lukas Klostermann spurned a great chance to put the second-division side ahead.
Wolfsburg made them pay after 19 minutes, with Kevin De Bruyne unlocking the defence for Daniel Caligiuri to fire home from inside the box.
Timm Klose made it 2-0 to Wolfsburg 11 minutes after the restart, and that is how it remained.
Munich, Gladbach and Wolfsburg will join fellow top-tier teams Bayer Leverkusen, Borussia Dortmund, Freiburg and Hoffenheim in Sunday's quarter-finals draw.
Bielefeld are the only non-Bundesliga side remaining in the competition.
