Pep Guardiola's side have now won all five of their games ahead of the new season, scoring 22 goals in the process, with Luuk de Jong's penalty for Gladbach representing the first time they have conceded.
The Dutchman netted at the end of the first 30-minute half at Borussia-Park after Franck Ribery, Philipp Lahm and Thiago Alcantara had put Bayern firmly in control.
Ribery turned provider for Arjen Robben in the second period before Thomas Mueller put the gloss on the result in the last minute.
The Bavarians are expected to be major contenders domestically and in the UEFA Champions League this season and their ability was showcased in the first goal in the 17th minute as Robben lifted a clever chip into Ribery's path and the Frenchman finished with aplomb, volleying past Marc-Andre ter Stegen on the turn.
Ribery then pounced on a loose pass from Granit Xhaka before squaring for Lahm to tap home and Thiago chested Jerome Boateng's cross home as Bayern struck three times within nine minutes.
De Jong gave his side a faint glimmer of hope, stroking home from 12 yards after Diego Contento scythed down Patrick Herrmann.
But Bayern were not to be denied and, 11 minutes into the second period, Robben nodded in Ribery's cross unmarked before Mueller converted with the last kick of the game to keep Guardiola's ominous start going.
The two sides will meet again in just three weeks to begin their respective Bundesliga campaigns at the Allianz Arena.