Pep Guardiola's side looked to be heading for a stuttering draw against Hoffenheim to go with their opening match defeat to Lyon.
But up popped veteran Silva on 87 minutes to seize on a mistake and lash the ball home for the crucial deciding goal.
Playing their first home Champions League game ever, Hoffenheim got off to an incredible start.
Inside a minute a low through ball from Kerem Demirbay caught the visiting defence flat-footed and Algerian Ishak Belfodil kept his cool to score.
Their young coach Julian Nagelsmann had promised to attack – but nobody expecteded that – particularly not Pep Guardiola.
Just 43 seconds had passed and it was the quickest goal City have ever conceded in this competition.
Luckily for him, the lead last just six minutes as David Silva opened up the German defence to send Leroy Sane clear down the left.
His low cross should have been cleared but Sergio Aguero nipped in to score for a fifth straight Champions League away game.
City – needing a win after their shock opening day defeat to Lyon – should have gone ahead with Raheem Sterling denied by the legs of Oliver Baumann.
The keeper also made a flying save to tip Aguero's delicate chip over the bar – while the Argentine fired another couple of efforts off target.
But there were still warning signs at the other end as Aymeric Laporte's woeful back pass let Belfodil in again but Ederson saved with his legs.
Early in the second half David Silva put a shot into the side-netting after a good cross by Laporte.
Sub Bernardo Silva teed up Aguero for a header which lacked power – allowing Baumann to get across and save.
Then City were screaming for a penalty when the visiting keeper sent Sane flying but amazingly the Slovenian referee waved away the appeals.
But just as City looked to be heading for a damaging draw, they snatched the win when
Bernardo Silva's cross from the left was not cleared Silva nipped in to score on 87 minutes.
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