The Premier League champions and current leaders, urgently needing a win after their opening week Group F defeat at home by Olympique Lyonnais, had been rocked by an Ishak Belfodil goal after just 44 seconds.
However, the visitors struck back just seven minutes later as Silva picked out Leroy Sane brilliantly and the German winger held it up within the six-yard box before finding Aguero, who eventually fired home.
Baumann produced a stunning one-handed stop to thwart Aguero again before the break, but the hosts regained a foothold in the second half.
Hoffenheim were left on one point with Lyon, on three points, hosting Shakhtar Donetsk later on Tuesday.
Valencia striker Rodrigo Moreno says the players won't be underestimating Champions League opponents Manchester United. "You can not make the next steps if you don't suffer or live this kind of experience, where you have to fight against everything".
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Gallagher confirmed via phone to The Associated Press that it was her, and she consented to the use of her name. The entire exchange was caught on camera (video above).
Guardiola, back on the sidelines after serving a one-match ban against Lyon, leaped off the bench in fury when City were denied a penalty when Baumann brought down Sane in full flight in the area.
The visitors pushed for a victor, with Aguero and Raheem Sterling both thwarted by Oliver Baumann in the Hoffenheim goal.
"He's coming out in press conferences constantly having a go at players, having at go at people above him because he's not getting what he wants", said Scholes.
Justice was served, though, when David Silva robbed the ball from Stefan Posch inside the Hoffenheim area in the 87th minute, shooting past Baumann for the victor.
The Citizens are now second in group standings with three points from two matches. "Now it's in our hands unlike before and, of course, we can not make the mistake we did against Lyon", said Guardiola. They are certainly a team in form and are playing at home - it will certainly be a hard game for us.