Bayern Munich will face fourth-tier side Rodinghausen in the second round of the DFB-Pokal.
The Bundesliga champions needed a late Robert Lewandowski goal to win at Drochtersen/Assel in the previous round, the striker's 82nd-minute effort eventually settling the tie.
And Bayern will again travel to take on minnows in the competition after Sunday's draw sent them north to play against Rodinghausen.
Borussia Dortmund also struggled to clear the first hurdle, with captain Marco Reus hitting a 120th-minute winner away to Greuther Furth.
Next up for Lucien Favre's men will be a home game against Union Berlin, while one of the ties of the round sees Borussia Monchengladbach at home to Bayer Leverkusen.
The most eye-catching fixture, however, will see RB Leipzig take on Hoffenheim, pitting Julian Nagelsmann - who is currently in charge of the latter - against his future employers.
There is a further all-Bundesliga clash between Hannover and Wolfsburg, while top-flight rivals Augsburg and Mainz have also been drawn together.
Holders Eintracht Frankfurt, who defeated Bayern in the final at the end of last season, are already out having been surprisingly beaten by Ulm.
