"We are of course satisfied. The whole team staged a good performance. As we created and finished off beautiful goals," Bayern head coach Jupp Heynckes said.
"We tried hard but Bayern is just too big for us. Six conceded goals are too much but it was a good learn process for me," Paderborn head coach Steffan Baumgart said.
Elsewhere, Bayer Leverkusen booked their place in the semis as well after bouncing back from 2-0 to win 4-2.
Bremen grabbed a perfect start into the game and established a two-goal lead before Leverkusen's Julian Brandt scored twice to restore parity.
The "Werkself" had the last laugh in the overtime as Karim Bellarabi and Kai Havertz secured the victory on home soil.
Eintracht Frankfurt host Mainz and Schalke encounter Wolfsburg to complete the round of the German Cup last eight on Wednesday.
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