The first real opening of the game fell to Robert Lewandowski, who saw his effort from close range blocked on 18 minutes by some solid defending inside the penalty area.
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Max Kruse wasted the first-half's best opportunity when he failed to get the better of Manuel Neuer when played through one-on-one with the Germany international. The stopper stayed alert and dived down to his left to keep out the effort to ensure that the two teams went into half time all square.
Bayern upped the pressure in search of a goal following the restart, although Christoph Kramer came within inches of giving Gladbach the lead on 52 minutes, only for his shot to be kept out by Neuer.
Neur had to be on guard once more shortly after, this time denying Raffael's free kick which was heading into the back of the net if not for his intervention.
To cap off his fine evening, the Bavarian side's number one frustrated Raffael again 10 minutes from time, keeping out the midfielder's strike in what proved to be the last chance of the game.
The result ensures that Bayern remain four points clear at the top of the table after nine games.