Filip Daems' first-half penalty was enough for the home side to beat Augsburg for the first time at the fourth attempt in Germany's top division.
''It was important for us to get the three points today, to put on a good performance,'' said Daems, who has now converted 11 penalties in succession for Moenchengladbach.
The Belgian defender sent the goalkeeper the wrong way in the 27th minute, after Augsburg midfielder Kevin Vogt was shown a straight red for bringing down Peniel Mlapa in a tussle to concede the spot kick.
''You can give the penalty, the red card was excessive,'' said Augsburg coach Markus Weinzierl. ''We made one mistake. It was decisive.''
Mlapa almost made it 2-0 three minutes later when his shot came back off the post with the goalkeeper beaten.
Moenchengladbach dominated against 10 men but failed to convert a host of chances.
Mike Hanke flashed his shot wide after a well-worked team move on the hour, and went even closer in the 73rd, when his effort crashed back off the post.
The visitors' best chance came in the final minute, when Marc-Andre ter Stegen denied Knowledge Musona an unlikely equalizer from point-blank range.
Ahead of the rest of the weekend's games, Augsburg remains three points from safety in the relegation playoff place. Moenchengladbach is two points ahead of Eintracht Frankfurt in the last European qualification place. Frankfurt hosts fourth-place Schalke on Saturday.
''We let too many chances go begging. We had so many chances to get the second goal,'' said Moenchengladbach coach Lucien Favre. ''But I saw a lot of positive things. We deserved to win.''