The returning Douglas Costa started on the bench as Bayern went with a front-four of Serge Gnabry, Thomas Muller, Kingsley Coman and Robert Lewandowski.
Bayern wasted no time to go ahead after a series of passes near the area eight minutes in had Lewandowski and Coman combining to set-up Muller for a smart finish.
Corentin Tolisso could've given Bayern a second a few minutes later with a deep delivery from Lucas Hernandez, but was not able to get Arminia goalkeeper Stefan Ortega to work.
The second would arrive five minutes to the half-hour mark with a one touch from Lewandowski resulted in a cracking finish from Leon Goretzka's square ball.
Lewandowski finished the first half with a brace right on the stroke of halftime as the Pole brought down a cross from Muller to slam home with a wicked deflection.
Bayern refused to let the foot of the accelerator six minutes from halftime, and found a fourth after Muller completed his brace with an exquisite curler whilst Lewanwdoski cracked the post earlier on.
Bielefeld pulled one back on 58 minutes after good initiative from Fabian Klos ended with a low ball to striker-partner Ritsu Doan, who did the rest with a snap finish from an acute angle.
The Bavarians threw in a double substitution inside the closing phase with the game virtually wrapped up, as Javi Martinez and Costa replaced Gnabry and Goretzka respectively.
Bayern finished the match with ten players in the last 14 minutes after Tolisso walked the plank for a poor challenge outside the area on Klos.
The champions cracked the woodwork for the second time later on after Martinez got on the end of Muller's flick on, leaving Bayern to an emphatic triumph.