The Bavarians were pushed all game by Gladbach, who produced 16 shots and 1.53xG but were unable to find the back of the net despite two notable big chances.
Bayern, on the other hand, showed their class with their defence holding firm all game and bagging two goals from 24 shots and 2.53xG created.
They hosts opened the scoring in the 32nd minute when Michael Olise cut a lovely cross onto the head of star striker Harry Kane to score his 25th Bundesliga goal of the season.
Kane was back in the lineup after serving a one-game suspension and instantly proved his worth once again.
"It's been a long time coming," Kane said of his first major trophy win. "It means more than any of the goalscoring awards, for sure.
"There's no secret that there has been this one thing that has been missing from my resume.
"It was a weight on my shoulders and now it's been lifted. I've had plenty of individual accolades and been close on so many occasions to trophies, but for one reason or another, it hasn't quite worked."
Olise then got on the scoresheet himself late on the game to secure the points and ensure that Bayern Munich could celebrate their latest title win on home soil.
Elsewhere in the Bundesliga on Saturday, Mainz hammered Bochum 4-1, while Werder Bremen and RB Leipzig cancelled each other out in a dull 0-0 draw.
Freiburg snuck past Kiel 2-1 and Union Berlin were thrashed 0-3 at home by Heidenheim, with Wolfsburg and Hoffenheim playing out to a dramatic 2-2 draw.
Bayern Munich's honorary president has firmly dismissed the possibility of Nicolas Jackson making a permanent move from Chelsea, stating there's no way the striker will fulfill the required conditions for the transfer.
Bayern Munich's honorary president Uli Hoenes has been hyper cricital of Newcastle United's spending in the recently concluded transfer window, especially in regards to their purchase of Nick Woltemade from Stuttgart.
Cody Gakpo has opened up about the intense transfer speculation linking him to Bayern Munich, admitting the situation was "hectic and stressful" before ultimately deciding to extend his stay at Liverpool.
Luis Diaz has made a flying start to life at Bayern Munich after his high-profile move from Liverpool, with the Colombian winger quickly proving why the German champions fought hard to sign him.
