Lewandowski scored four times in Bayern's 4-3 win over Hertha Berlin in its last match before the international break and struck twice for Poland in a victory over Bosnia-Herzegovina in midweek.
The prolific striker took his goal tally for the season to nine goals in seven matches with a first-half double at Bielefelder Alm after playing a big part in Thomas Muller's opener.
He then set up Muller for Bayern's fourth as the champion, which conceded to Ritsu Doan's low drive before losing Corentin Tolisso to a straight red card, made it four wins in a row in all competitions and climbed into second place.
Lewandowski played in Muller with a first-time pass in behind and the attacker converted just eight minutes in after his initial pass to Kingsley Coman – earlier denied a penalty – was cut out.
Tolisso and Muller wasted good opportunities to extend Bayern's lead before clinical striker Lewandowski did exactly that with a thumping strike from 18 yards.
The pair was at it again at the end of the first half as Muller squared to Lewandowski to score his second from a near identical position to the first, helped by a telling deflection.
Lewandowski was denied a third by the crossbar early in the second half but crossed for Muller to volley in from six yards out 100 seconds later.
Bielefeld, previously unbeaten in 10 home games in 2020, did manage to pull one back on the counter just before the hour mark through Doan's shot across Manuel Neuer.
Tolisso was then dismissed with 14 minutes to play for bringing down Fabian Klos as the last man, but Hansi Flick's men came closest to scoring the sixth goal of the match as substitute Javi Martinez nodded against the woodwork late on.