City had previously fallen victim to a late Cristiano Ronaldo goal during their 3-2 loss to Real Madrid, and another setback against the German outfit would leave the Premier League side facing another elimination from the group stages of the tournament.
Roberto Mancini named an attacking lineup against Jurgen Klopp's men, with Edin Dzeko and Sergio Aguero being supported in attack by David Silva and Samir Nasri, while Yaya Toure was given the task of inspiring his team from midfield.
It was City who started the sharper of the two sides, with Edin Dzeko testing Roman Weidenfeller from distance, but it didn't take long for Dortmund to hit their stride and stamp their authority on proceedings.
The home side attempted a response through Aguero, who brought a decent save out of Weidenfaller, but it was Dortmund who looked the more impressive, with Neven Subotic sending a shot flying past the out-stretched reach of Hart, but fortunately for the England stopper, the ball just missed the far post.
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As the half-time whistle approached, the fluidity of Dortmund's play intensified with City struggling to get close to their opposition. They were left to rely on the heroics of Hart, who was required to pull off consecutive high-quality stops to deny Gotze and Ilkay Gundogan.
The German side returned after the break with the same enthusiasm that they ended the first, forcing the City back line onto the defensive at every opportunity, before Hart being forced into action once again to prevent a Gotze shot finding the top corner.
Mancini soon decided that enough was enough and brought on the more defensively-minded Alexander Kolarov in place of Nasri, but the change didn't have the desired effect, and two minutes later, City fell behind.
Jack Rodwell's stray ball was intercepted by the energetic Reus, and the German advanced on goal before coolly clipping the ball over the helpless Hart, who had finally seen his clean sheet taken by a rampant Dortmund outfit.
The City faithful were calling for an immediate response, but their team could do little to stem the Dortmund tide, with Hart, who was undoubtedly the man of the match, saving from Reus and Gundogan.
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Despite Dortmund's domination, City were still in the game while the deficit remained at just the one goal, and Mancini introduced Mario Balotelli with nine minutes remaining to try to inspire his side to what would be a dramatic, if not undeserved, share of the spoils.
The Italian soon got himself into the action, but City's quest for parity was aided by a questionable decision from the referee, who awarded the English side a penalty after deciding that Subotic had deliberately handled the ball inside the area.
That allowed Balotelli to step up and confidently slot the ball past Weidenfeller, much to the displeasure of Klopp's side who could justify their belief that they had been hard done by after an attacking display that had earned them plenty of admirers from the home crowd.
While the draw ensured that City remained in contention in the group, they quickly lost ground on both Madrid and Dortmund after falling to a demoralising defeat away at Ajax, which left City effectively requiring three victories in a row to progress through to the knockout stages.
However, despite fighting back to draw with the Dutch side at the Etihad Stadium, it all but eliminated City from the competition with two games remaining, while Dortmund enjoyed a memorable run to the final at Wembley before being ousted by domestic rivals Bayern Munich.