The first goalscorer of the night then turned provider in the 25th minute, delivering the cross for Robert Lewandowski to rifle home and double Bayern's lead.
On 42 minutes, Joshua Kimmich beat the offside trap to apply the finish to Mats Hummels's ball over the top and Corentin Tolisso headed a fourth just before the hour.
The scoreline was given more gloss late on through Arjen Robben, who scored from 20 yards out on 86 minutes and then tapped home from close range two minutes later.
SC PADERBORN (4-1-3-2): Ratajczak; Boeder, Schonlau, Strohdiek, Herzenbruch; Krausse; Zolinski, Wassey (Tietz 45'), Antwi-Adjej (Bertels 66'); Ritter (Klement 74'), Michel
BAYERN MUNICH (4-1-4-1): Ulreich; Kimmich, Sule, Hummels, Alaba; Vidal; Robben, Muller (Tolisso 32'), James (Rudy 67'), Coman (Ribery 81'); Lewandowski