Lewandowski brace sends Bayern second
Treble winners Bayern started the day in mid-table following a shock defeat to Hoffenheim last month, but victory in Bielefeld was enough to propel them back up to second place.
The champions burst out of the blocks and had an early penalty appeal turned down before Muller bundled in the opener on eight minutes.
Lewandowski doubled the lead shortly afterward, smashing the ball in from the edge of the area after a sharp cross from Leon Goretzka.
The Poland striker linked up with Muller to make it 3-0 just before half-time and returned the favour after the break with a pinpoint cross to set up Muller's second.
"The first 45 minutes were crazy, we played really well. We knew that the first game after the international break would be really important," Lewandowski told Sky.
Japan winger Ritsu Doan then pulled one back for Bielefeld on the break, the PSV Eindhoven loanee netting his first Bundesliga goal since moving to Germany in the summer.
Yet despite a late red card for Corentin Tolisso, Bayern were untroubled in the final stages and can now turn their attention to Wednesday's Champions League opener against Atletico Madrid.
Hansi Flick's side now sit level on points with third-placed Borussia Dortmund, who snatched a late 1-0 win at Hoffenheim earlier on Saturday.