City got the better of the Bundesliga outfit 2-1 away from home in Germany in the Champions League Group D.
Lars Stindl put Monchengladbach in the lead at Stadion im Borussia-Park in the 54th minute, but Nicolas Otamendi volleyed home to restore parity for the Premier League outfit in the 65th minute.
Argentina international striker Aguero scored the winner late on from the penalty spot, as City maintained their chances of progressing to the last 16 of the Champions League this season.
After the game, Aguero and midfielder Toure took to Twitter to revel in the triumph.
It was vital we won today. It wasn't easy but we did it and took three important points. C'mon, City!— Sergio Kun Aguero (@aguerosergiokun) September 30, 2015
Important win!! Looking forward to the next games! #ComeOnCity— Yaya Touré (@YayaToure) September 30, 2015
Over the course of the 90 minutes at Stadion im Borussia-Park, City had 65% of the possession, took 26 shots of which just seven were on target, and earned 11 corners.
Manuel Pellegrini’s side are third in Group D at the moment with three points from two matches, three points behind leaders Juventus.