The Premier League Champions' European dream ends for another season after a poor campaign, while Jurgen Klopp's side continue to impress as it wins Group D ahead of Real Madrid.
Julian Schieber’s second-half finish from close range was enough to see off the visitors, after Dortmund had the better of the scoring chances throughout the game. The result means Roberto Mancini’s side finishes bottom of Group D without a win and don't even qualify for the UEFA Europa League group stage, while Dortmund goes through to the knockout stage as winner of the vaunted Group D.
It was a very quiet start to the game, with both sides exchanging lengthy – but non-threatening – periods of possession, and it took until the 12th minute for a shot as Oliver Kirch drove straight at Joe Hart from 20 yards out.
The visitors eventually fashioned an opening of their own, as Edin Dzeko slid the ball across the six-yard box looking for Carlos Tevez, but Marcel Schmelzer was able to snuff out the danger.
Dzeko then tested Roman Weidenfeller, drilling a low effort from distance and forcing the Dortmund shot-stopper to parry wide, before the hosts had a glorious chance to take the lead. Marco Reus cut into the area, blasting a left-footed effort towards Hart’s near post which the England international managed to tip on to the woodwork and behind.
City nearly went in front straight after halftime as Dzeko met Samir Nasri’s cross, heading straight at the goalkeeper when he looked odds-on to score.
Just after Sergio Aguero was introduced by Mancini, the deadlock was broken in the 57th minute as the hosts took a deserved lead. Substitute Jakub Blazczykowski burst down the right and slid an excellent cross into the path of Schieber, who arrived at the far post to poke the ball into the net.
City switched to a back three with the introduction of Mario Balotelli and Pablo Zabaleta, as Tevez produced a fine piece skill to work space in the box and force a save from Weidenfeller.
Moritz Leitner had a superb chance to make it two after the impressive Blazczykowski pulled back, but the midfielder could only steer his effort wide.
Substitute Robert Lewandowski then forced a save from Hart after shooting from a tight angle, before Weidenfeller saved a left-footed Aguero strike at the other end as the hosts saw out the win and cemented their place atop the Champions League's toughest group.