It was the visitors who were gifted the opportunity to break the deadlock in just the third minute when Jan-Ingwer Callsen-Bracker was spotted punching the ball in the box as he looked to clear a corner.
Monchengladbach finished the first half strongly, but the visitors missed good opportunities either side of the break as Manninger comfortably denied Roel Brouwers and Andre Hahn.
Raul Bobadilla put Augsburg ahead just a few minutes after Hahn's miss when Alexander Esswein picked out the Argentine forward, whose powerful strike went in off the crossbar to leave Yann Sommer helpless.
Augsburg soaked up the pressure applied by Monchengladbach as the hosts produced an impressive defensive display to stifle the visiting side's creative players.
Monchengladbach's best chance fell to Thorgan Hazard late on, but the young Belgian was unable to hold his nerve in the box, as Manninger made a fine save to secure the points for the hosts.