Coming off a vital 3-2 win over Borussia Dortmund, which has virtually sealed a 34th Bundesliga title, Bayern started well, and Lennart Karl had a strike chalked off for offside inside 10 minutes.
Despite failing to really create anything else before the half-hour mark, the hosts didn’t give Gladbach any opportunity to play out, and gradually crescendoed to an opener.
Leon Goretzka received the ball from Kim Min-jae on the edge of the area, and cheekily chipped it through to Luis Diaz, who gracefully volleyed it into the corner.
With the pressure taken off, chances came more readily for Bayern after that, with Nicolas Jackson - deputising for the absent Harry Kane - and Konrad Laimer both going close before their side’s second in first-half stoppage time.
Jackson turned brilliantly to drive Bayern up the field and shift it out to Diaz, who passed it back across the box for Laimer to power into the far corner.
It wasn’t all good news for Bayern, as Manuel Neuer was withdrawn at half-time with a possible injury concern.
Gladbach’s promising start to the second half quickly evaporated when Rocco Reitz hauled down Jackson when through on goal, and saw referee Robert Schröder not only point to the spot but produce a red card for him.
Jamal Musiala was elected to step up and fully mark his recent return from a lengthy injury by rolling in his first league goal of the season.
Bayern used their cushion to introduce 17-year-old debutant Maycon Cardozo, and they looked to comfortably see out the rest of the match, scoring a fourth when Jackson diverted Karl's low ball into the six-yard box in off the near post.
But the travelling Gladbach fans did have something to celebrate, as a quickly-taken free-kick was diverted onto the post by Fabio Chiarodia, but then turned in on the rebound by Wael Mohya - making him the club’s youngest-ever Bundesliga scorer.
It’s a fifth consecutive Bundesliga victory for Bayern, and sees them open up a 14-point gap to second place ahead of the rest of matchday 25.
They face Dortmund-killers Atalanta in the next round of the UEFA Champions League, while Gladbach will be fully focused on their league run-in, especially as they sit just three points from the relegation play-off spot.
Flashscore Man of the Match: Luis Diaz (Bayern)
