Jurgen Klopp's side are on a four-match losing streak in the league but are on course for what could be a watershed win thanks to a reported Bayern transfer target.
Having passed a late fitness test to start for the Bavarians, Arjen Robben was immediately involved as he forced Roman Weidenfeller into smartly tipping over his crossbar, before slicing a second effort high.
A lively opening set the tone for what was to be an end-to-end first half, and Dortmund soon threatened themselves as Henrikh Mkhitaryan ran across the Munich defence only to drag a shot narrowly wide.
Manuel Neuer was typically rapid off his line to thwart Pierre-Emerick Aubameyang on the half-hour mark, but Dortmund did lead less than a minute later as Reus finished off a swift counter-attacking move.
The German international midfielder, who is rumoured to be high on Bayern's January wishlist, made a late burst in from the left to get in front of Boateng and head Aubameyang's cross beyond Neuer.
Table-topping Munich are unbeaten in the league this season and came close to equalising prior to the break when Weidenfeller saved again from Muller, and when Sven Bender blocked Robben's shot on the line.