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.
Pep Guardiola's side had got off to a awful start, conceding after just 44 seconds when Ishak Belfodil opened the scoring, but Sergio Aguero quickly equalised.
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.
"It's too early to be defining but it certainly has the feeling that a lot more is at play than the three points".
In the first meeting between the sides, the Bundesliga outfit wasted no time in forging ahead, Ishak Belfodil coolly converting following Kerem Demirbay's throughball.
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Tuesday's game will be the first time that Hoffenheim and Manchester City have ever played each other.
The second goal arrived midway through the first half, with Dybala firing home from close range after Blaise Matuidi's initial effort was saved.
Asked about the penalty, Guardiola, who had been back on the touchline after serving a one-match European ban, said he would not comment because he did not want to end up back in the stands.
But City finally got the victor after Stefan Posch was caught dallying inside the area, allowing Silva to find the bottom-right corner with typical assuredness.
City's progress to the group stage is still far from certain with Group F intriguingly balanced.
Manchester City have conceded two or more goals in each of their past four Champions League games; they last conceded at least two goals in five consecutive matches back in March 2014.