The Bavarian giants have been made to wait at least another week for a sixth successive title, though, as closest challengers Schalke 04 beat Freiburg earlier in the day.
Top scorer Lewandowski was played in on goal by Muller and made no mistake by smashing the ball past Roman Burki, who would pick the ball out of his net a further four times over the next 40 minutes.
Ribery had a goal ruled out by VAR moments later but it did not take long for a legitimate second to follow, as David Alaba and Rodriguez exchanged passes for the latter to slot past Burki.
A third Bayern goal soon arrived, however, with Rodriguez chipping an inviting cross into the middle for Muller to volley home after Gonzalo Castro gave away possession in midfield.
Klassiker bragging rights were Bayern's by this point, but they were not finished there as Lewandowski poked a loose ball over the line following some pinball in the box, before Ribery dinked the ball over Burki after some more intricate link-up play.
Having built up their biggest half-time lead in five years, the hosts never really had to get out of first gear in the second 45.
Lewandowski was denied a hat-trick by Burki after turning and shooting on the edge of the box, while up the other end Ulreich barely had to break stride to deny Lukasz Piszczek.
A frustrating evening for Michy Batshuayi was summed up when a ball towards him in the middle was slightly overhit, and Bayern were not in a forgiving mood as they went on to bag a sixth.
Lewandowski was given the chance to complete his treble, this time making the most of the time and space afforded to him by tapping the ball over the line from a Joshua Kimmich cutback, putting Bayern on the brink of yet another title.
BAYERN MUNICH (4-3-3): Ulreich; Rafinha, Boateng, Hummels, Alaba (Kimmich 46'); Muller, Martinez, Rodriguez (Thiago 65'); Robben, Lewandowski, Ribery (Rudy 69')
BORUSSIA DORTMUND (4-2-3-1): Burki; Piszczek, Sokratis, Akanji, Schmelzer; Castro (Weigl 29'), Dahoud; Pulisic (Philipp 74'), Gotze (Sahin 77'), Schurrle; Batshuayi