Formidable at the Allianz Arena with five consecutive home wins, Bayern dominated the first half, but were forced to wait until the 43rd minute before finding the breakthrough.
The visitors fought hard to frustrate the runaway Bundesliga leaders in the opening exchanges, albeit without creating anything themselves.
The first clear chance for the hosts came just before the half-hour mark when Josip Stanišić picked out Lennart Karl with a pinpoint cross, but he failed to convert an easy tap-in as the ball struck the face of the post before bouncing clear.
Harry Kane should’ve opened the scoring shortly after as he rounded the goalkeeper, but he couldn’t find the back of the net with the angle against him.
Just when it looked like Die Eisernen could go in level at the break, the dam quickly burst as they conceded two goals on the verge of half time.
Michael Olise had threatened on the right flank throughout the half, and he stepped up to find the breakthrough as he cut inside onto his left foot before arrowing a curled finish into the far corner.
The visitors needed to make it to the break, where they could regroup, but they were caught in stoppage time when Frederik Ronnow missed his punch as he came for a cross, leaving Serge Gnabry to smash a decisive volley home at the near post.
The half-time break could only offer a brief respite for the visitors, as any hopes of a comeback were quickly eradicated shortly after the restart.
Despite facing pressure from three Union defenders, Kane somehow collected Konrad Laimer’s pass before turning and finding the bottom corner with absolute precision.
Coming into the game with 93 Bundesliga goals already this season, Bayern’s relentless attack continued to press, and Gnabry grabbed his second after beating Ronnow at the near post with sheer power.
The result means Union are now winless in their 14 total H2Hs with Bayern in the Bundesliga, and look set for a mid-table finish as they sit equidistant between the top seven and bottom three, with seven points separating them either way.
Bayern, on the other hand, move 12 points clear of Borussia Dortmund and remain clear favourites to retain the Bundesliga title.
Flashscore Man of the Match: Serge Gnabry (FC Bayern Munich)