Joe Hart saved Borussia Monchengladbach's penalty before Sergio Aguero fired home City's winner.
Manchester City boss Manuel Pellegrini heaped praise on Aguero and Hart as the Citizens came from a goal down to earn their first Champions League win.
Argentina international Aguero scored a last-minute penalty following Hart's penalty save at the other end, and after the tie Pellegrini expressed his delight with the pair.
“Joe made three very important saves,” said the City boss, as the Daily Mirror reported. “He saved a penalty. After that he also made brilliant saves. The performance of Joe was very important for us.
“For Sergio, it’s not easy to score a penalty in the last minute, but he did it. He had chances to score before that and we know how important Sergio is for our team.
“I think it was a very important win. They deserved to be winning 1-0, but for the last 25 minutes we had a very strong reaction. We scored the two goals and had other chances.”