Yet they kept their patience and Silva's quick thinking, robbing central defender Stefan Posch in the box and shooting home a sharp victor took them on to three points in the group.
However, it took only 43 seconds for Pep Guardiola's side to go behind, with Ishak Belfodil firing through the legs of Ederson after the City backline was split open far too easily.
City hit back nearly immediately when Silva's pass split the Hoffenheim defence and found Leroy Sane who put Aguero into space to tap home the equaliser on eight minutes.
"It's too early to be defining but it certainly has the feeling that a lot more is at play than the three points".
Without the injured Dele Alli, Spurs' hopes of an upset look minimal, but a conclusive result either way could shape both of these sides' seasons.
Tuesday's game will be the first time that Hoffenheim and Manchester City have ever played each other.
Raheem Sterling, after a lightning end-to-end break, and Aguero went close to putting City ahead as they piled on the pressure. City can not afford to have one eye on their trip to Anfield on Sunday, but their squad is deep, and I expect them to get their Champions League challenge back on track.
Guardiola was unhappy at Leroy Sané being denied a penalty when Oliver Baumann appeared to pull him down in the second half but the City manager - who was serving a touchline ban when City lost to Lyon at the Etihad - refused to discuss this afterwards.
Later in Group F, Lyon was hosting Shakhtar Donetsk.
When asked by reporters if he wants City to win the Champions League to complete Silva's list of honours at the highest level, the Spaniard replied : "I think everyone deserves to win it".
The match was destined for a draw before David Silva sniffed out a goal from nothing just three minutes to stoppage time to hand his side a deserved victory.