Lionel Messi set Barcelona on their way with the opener in the second half to kill off any chance of City producing an heroic comeback from the 2-0 defeat in the first leg at the Etihad Stadium.
To compound City's misery Pablo Zabaleta was sent off late on for dissent after confronting the referee over his failure to award the visitors a penalty.
Vincent Kompany pulled a goal back for the 10 men in the final minute, but there was still time for Dani Alves to grab the winner for Barcelona in the closing seconds.
After a bright start from City they had a lucky escape on nine minutes when Joleon Lescott appeared to bring down Messi inside the box, but much to the relief of Joleon Lescott referee Stephane Lannoy waved away the home side's penalty appeals.
Three minutes later Messi set off on a run past a couple of challenges and nicked the ball off Joe Hart, but Kompany got back to clear the danger just when it looked the Argentine ace was about to roll the ball into an empty net.
City had a sight of goal on 17 minutes when Aleksandar Kolarov got down the left and cut the ball back for James Milner, who side-footed his effort across the face of goal.
A minute later City had another stroke of good fortune when Barcelona had a goal from Neymar disallowed for offside even though it looked like Alba was onside when he collected the pass from Xavi before crossing for Neymar.
City went close to scoring on 36 minutes when David Silva found space on the left and he cut inside and fired over the top when he should have hit the target at least.
Barcelona had a great chance to break the deadlock on 39 minutes when Neymar capitalised on a slip from Kolarov to go clear on goal, but his effort was superbly turned round the upright by Hart at his near post.
From the resulting corner Hart again came to City's rescue when when he kept out Xavi's sliding shot after Messi picked out the midfielder's run into the box.
City wasted their best opening of the half four minutes before the break when Silva brilliantly flicked the ball into the path of Samir Nasri inside the box, but the Frenchman fired his shot straight at Victor Valdes.
Barcelona went close to scoring right on the stroke of half-time when Neymar got through on goal from Messi's pass and after being pushed wide by Hart he beat the keeper and fired in a shot which was headed off the line by Fernandinho.
Barcelona were inches away from scoring on 51 minutes when Lescott gave the ball away to Messi and the Barcelona star beat the City defender inside the box before driving his low shot off the base of the post.
City then went straight up the other end and substitute Edin Dzeko got on the end of Kolarov's cross and his header goalwards was brilliantly tipped over the top by Valdes at full stretch.
The visitors had another chance to score on 54 minutes when Kolarov's cross fell to Zabaleta inside the box, but he sliced his shot wide of the target.
Barcelona broke the deadlock on 67 minutes when Lescott made a mess of trying to cut out a Fabregas pass and the ball fell to Messi, who clipped the ball past Hart with clinical ease.
City felt they should have had a penalty 12 minutes from time when Dzeko appeared to be tripped by Gerard Pique, but the referee ignored their appeals and things got worse for City when Zabaleta was sent off for a second bookable offence for taking his protests too far.
Kompany drew City level on the night a minute before the end when he fired home from inside the six-yard box when he got on the end of Dzeko's header.
However, there was still time left for Barcelona to grab a winner as Alves scored the second time in the tie as he blasted home from inside the box after being teed up by Andres Iniesta.