The German giants, who suffered a shock defeat to Borussia Monchengladbach last week, were determined to bounce back and delivered a punishing first-half display that secured their place at the top of the table.
Bayern wasted no time in asserting their dominance, with Eric Maxim Choupo-Moting coming close to opening the scoring in the fifth minute.
The Cameroon striker would eventually find the back of the net in the 31st minute, looping a header over Union goalkeeper Frederik Ronnow from a Kingsley Coman cross.
Bayern Munich
Coman would then turn scorer himself, rounding Ronnow to double Bayern's lead.
Jamal Musiala capped off an outstanding first-half display with a goal on the stroke of half-time, turning in a Thomas Mueller cutback to make it 3-0.
Union, who had won five of their previous six league games, had no answer to Bayern's relentless attack and spent much of the game on the back foot.
Although they managed to limit the damage in the second half, with Ronnow making a string of impressive saves, they were ultimately unable to mount a comeback.
The victory sees Bayern remain in first place on 46 points, ahead of Borussia Dortmund on goal difference, and confirms their status as title favourites.
They will now turn their attention to their Champions League last 16 return leg against Paris St Germain on March 8, with the return of Sadio Mane providing a welcome boost to their attacking options.
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