But after being swept aside by a masterful Barca display in the first half, City at least gave themselves hope for the second leg of the last-16 tie as Sergio Aguero produced a brilliant reply.
City were left hanging on in the latter stages, however, after Gael Clichy was sent off for a second bookable offence and it needed an injury-time penalty save from Joe Hart to prevent further damage.
Lionel Messi had looked like giving the Spanish side a 3-1 lead to take back to the Nou Camp after being felled by Pablo Zabaleta but Hart pushed away his spot-kick and City breathed a sigh of relief.
That they might still be in the tie seemed unlikely at the interval, after Barcelona threatened to produce a performance much improved on the one that saw off City at the same stage last year.
Messi was at the centre of controversy after a late night casino visit on Sunday but – until his miss from the spot – it hardly seemed to take the edge off his game.
Without suspended midfield talisman Yaya Toure, City were never able to get a sustained grip on the game early on with Fernando – surprisingly preferred to fellow Brazilian Fernandinho – and James Milner in the central areas.
Milner had an early shot on goal from a free-kick after Aguero was hacked down by Javier Mascherano just outside the area but his low effort was blocked.
That was about as good as it got for City for a while as Barcelona soon moved through the gears.
Martin Demichelis, the villain of last year’s first-leg loss, twice rescued City as he blocked a shot from Messi and then headed away a Suarez cross after the striker surprisingly opted not to shoot.
Former Liverpool star Suarez had actually looked rusty in the early minutes with a few touches going astray, but he soon put that right in emphatic fashion after 16 minutes.
The Uruguayan’s luck changed when he got his head to a Messi cross and the ball rebounded kindly to him off Vincent Kompany. The angle was tight but he made no mistake with a lethal low strike.
Dzeko, one of City’s livelier players, headed a chance wide for the hosts but it was a rare opening.
Barcelona were brilliant in possession and Messi nutmegged David Silva inside his own half to launch a blistering attacking, ending with Neymar teeing up Suarez and Hart racing off his line to save.
Suarez’s second came on the half-hour after more trickery from Messi, jinking across the area and finding Neymar, and his low cross was turned in by a sliding Suarez.
It might have got even worse for City before the break as Neymar chipped Hart, only for Pablo Zabaleta to clear, and Dani Alves broke away and lobbed a shot on to the bar.
At times it resembled a training session for the Spanish side but the interval at least allowed City to regroup and they returned for the second half in more positive fashion.
Dzeko spurned two good chances to pull a goal back, heading wide when well placed and putting another effort straight at Marc-Andre ter Stegen.
Samir Nasri had an effort blocked and Aguero curled a shot wide after a good run.
But Barcelona remained a serious threat and Clichy fouled Ivan Rakitic after being caught out by the Croatian, earning the first of his bookings.
City gave themselves hope when Silva fed Aguero and the Argentinian showed typically nimble footwork to skip out of a challenge from Gerard Pique and lift the ball over Ter Stegen.
The crowd finally had something to cheer, but any thoughts of a famous fightback soon had to be moderated as Clichy received a second booking for catching Alves high.
It seemed a harsh decision but City coped well in his absence and looked to have seen out time when Zabaleta was penalised for bringing down his international colleague Messi.
Had Messi scored the resulting spot-kick, the challenge ahead might have been overwhelming, but Hart had the final say by beating away his shot. Messi was quick to the rebound but headed wide and the final whistle went seconds later.