Muller and Davies have been revelations for Bayern this term and both were as crucial as ever with a goal and an assist each, although their side's defending left plenty to be desired prior to a potentially pivotal match against Borussia Dortmund in Wednesday's (AEST) Der Klassiker.
There was nothing surprising about the pattern of the first period at Allianz Arena, however, and Bayern was fully deserving of its comfortable half-time lead of 2-0, the excellent Muller setting up Leon Goretzka before getting on the scoresheet himself.
Defensive lapses early in the second half showed a chink in Bayern's armour, however, as Martin Hinteregger netted twice in quick succession from corners after Robert Lewandowski had made it 3-0, but Davies's well-taken goal in the 61st minute was followed by an own goal by Frankfurt's Austrian centre-back to ensure a home victory.
Although Frankfurt managed to avoid a repeat of last week when it was behind after just 34 seconds, it was fortunate to keep Bayern at bay for as long as it did, Lewandowski hitting the crossbar and Benjamin Pavard going close in the early exchanges.
But there was no denying Goretzka in the 17th minute, the Germany international emphatically steering in a first-time effort after arriving on to Muller's inch-perfect cross.
Muller made it 2-0 just before the break, running clear of Frankfurt's offside trap as he collected Davies's left-wing delivery and squeezing the ball past the approaching Kevin Trapp, despite an awkwardly high bounce.
Lewandowski headed Kingsley Coman's cross in within a minute of the restart, seemingly wrapping up the points, but Bayern conspired to give Frankfurt a chance.
Hapless defending allowed Hinteregger to tee himself up for a close-range finish in the 52nd minute, and he then netted again a few moments later from another corner.
Yet Davies restored a modicum of calm to the Bayern bench just past the hour, finding the bottom-left corner after the ball broke kindly for him.
Hinteregger converted for a third time with 16 minutes to go, albeit it came in the wrong net as the ball ricocheted on to him and then into the goal after a driving run from Serge Gnabry.