City got a big scare in the 12th minute when Lewandowski, Mario Gotze and Marco Reus combined, with Gotze eventually taking a shot at goal that Joe Hart pushed onto his post and out for a corner.
Dortmund continued to play their hugely attacking and pressing game, with the hosts making runs at the Bundesliga champions' defence as well.
However, the next clear-cut chance of the contest fell to City in the 28th minute with Silva feeding Aguero, but Weidenfeller made a good save in keeping out the Argentine striker's shot.
The City duo once again combined in the 35th minute, with Aguero forcing Weidenfeller into conceding a corner with a fierce shot from outside the penalty area.
A minute later Neven Subotic tried his luck with a long-range effort that went narrowly wide of the City goal.
Hart was then called into action as he made two important saves inside a minute, first denying Gotze from just yards out before pushing the German playmaker's ferocious shot on to the bar and out for a corner.
Silva could have then given the Citizens the lead on the stroke of half-time, but he failed to find the target from just yards out, before Hart made another important save in injury time from an Ilkay Gundogan attempt.