Pep Guardiola's side had the majority of possession on Friday and created more than double that of their opponents as they extended their lead at the top of the table to 10 points.
Mario Gotze opened the scoring with a cool finish in the seventh minute, with Thomas Muller doubling the lead in the second half from the penalty spot.
Despite offering an impressive response, Monchengladbach were unable to get back into the game as Manuel Neuer made a couple of good saves and Patrick Herrmann hit the post.
The win moves Bayern 14 points clear of their third-placed opponents, giving Borussia Dortmund the opportunity to overtake Monchengladbach with victory over Augsburg on Saturday.
Bayern, the first team in Bundesliga history to win 15 of their first 17 matches, started with Gotze in a false-nine position and Xherdan Shaqiri, Muller and Thiago Alcantara offering support, while Mario Mandzukic was not included in the squad amid reports of a move to Juventus.
Gotze pulled his first opportunity wide of Marc-Andre ter Stegen's goal in the fifth minute, but made no mistake two minutes later with a crisp first-time finish.
Muller was released down the right by Rafinha and reached the byline before pulling the ball back to an unmarked Gotze, who calmly stroked the ball into the back of the net.
Bayern continued to dominate possession but were unable to work their way through the Monchengladbach defence, and the hosts eventually started to threaten at the other end.
However, Max Kruse again wasted a good opening as Neuer saved down low to deny the forward.
Thiago came close to doubling Bayern's lead early in the second half with a 25-yard strike, the Spaniard keeping his effort on target only for Ter Stegen to tip it round the post.
Eight minutes after the break the visitors did get their second goal as Granit Xhaka handled inside the penalty area.
Muller assumed responsibility from the spot and made no mistake in sending Ter Stegen the wrong way.
Neuer was called into action just after the hour and had to make two low saves.
When Monchengladbach did beat the goalkeeper, Herrmann's shot crashed against the post and bounced to safety.
Bayern negotiated the final 20 minutes comfortably and were able to introduce Arjen Robben following the Netherlands international's recovery from a knee injury sustained at the end of 2013.
