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Mario Gotze came close to breaking the deadlock just six minutes into the tie, but his finish drifted just wide.
However, the striker was able to find the target just a minute later after Thomas Muller played the ball through for him to bag his fifth goal for the club.
Bayern were able to extend their lead early in the second half when a Gotze effort hit the hand of Granit Xhaka in the box, giving the visitors a penalty, which Muller was able to convert.
Gladbach were denied by the post again shortly after as Patrick Hermann got the better of the Bayern defenders with his pace before clattering the woodwork.
The away side had a couple of half-chances for a third late on, but were unable to get the better of Ter Stegen in the home goal again.
The result leaves them 10 points clear at the top of the table, while Gladbach sit third.