The Argentine was brought down by Fabian Johnson in the 90th minute and kept his cool to hand City their first win and offer coach Manuel Pellegrini respite after his team lost their last two league games following a defeat by Juventus in their Champions League group opener.
"Maybe with a little bit of luck we won this game today," Pellegrini said. "But all the games we lost before, to Juventus, West Ham, Tottenham -- I don't think we deserved to lose them. But we did.
"Maybe today we did not deserve to win but we won," added the Chilean coach.
Gladbach, having waited 37 years for their first home game in Europe's premier club competition, stunned their big-name opponents with a 54th minute goal by Lars Stindl.
City, who have goalkeeper Joe Hart to thank for keeping them in the game with half a dozen superb saves including a penalty, drew level after Nicolas Otamendi's strike was deflected in by Andreas Christensen for an own goal in the 65th minute.
City launched into a late rally in search of a winner and were rewarded when the Argentine striker scored from the spot.
The result moved City up to three points with Gladbach still to earn any in Group D. Juventus are top on six after beating Sevilla 2-0, with the Spaniards in second place also on three.
Unbeaten at home against English opponents, Gladbach started the game well with Raffael firing over the bar in an opening salvo from the hosts.
In a frantic first half pace. Gladbach were lucky to earn a spot kick when the referee ruled that Raffael was brought down by Otamendi in a harsh decision.
Hart restored order, pulling off a great spot kick save to deny Raffael in the 19th minute before sending Aguero clear with a deep cross but the forward fired inches wide.
Hart twice more came to the rescue before the break, charging out of his goal to block Raffael's shot and then denying Patrick Herrmann in the 37th once more.
In the second half the England keeper picked up where he left off, palming away a fine curled shot by Raffael but could do nothing when Stindl drilled in with one touch after a superb cutback from Julian Korb in the 54th.
After the equaliser the visitors took control but had to wait until the 90th for Aguero to score from the penalty spot.
"We were a couple of minutes away," interim Gladbach coach Andre Schubert said. "Even a draw would have been a big sensation. We should have scored another either with the penalty or the chances we had. But even so we remained solid and dealt with the pressure well until the penalty."
(Reporting by Karolos Grohmann, editing by Pritha Sarkar)
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