His assist showed the qualities in Agüero’s creative game, his determination to win the ball, his athleticism to reach it and his vision to spot Silva’s run. City fans loved it, embarking on a brisk Poznan dance.  Swansea looked stunned, although their fans never stopped singing, never stopped supporting their team.

No wonder. They have waited so long for this moment; even the contrast in wealth, embodied by Agüero, could not silence their fans. They also departed south with the memory of their first-half display when Leon Britton, short of stature but big on ambition, stood out in midfield.

Swansea’s goalkeeper, Michel Vorm, who is in for a very busy season, also impressed with some of his saves. But he had little chance when Agüero gave City real focus, real belief.

For almost an hour, until Dzeko, Agüero and Silva triggered a mass Poznan celebration, City had struggled to break down the visitors.

Agüero made such a difference, bringing a sharper cutting edge, bringing team-mates into play and he has to start now. Dzeko made the breakthrough but it was Agüero who collected the headlines.

For almost an hour, Swansea’s natural width, a thrilling element to their promotion campaign, had been a counterpoint to City’s narrowness, even with Adam Johnson granted a rare start by Mancini. Showing little initial fear of their vaunted surroundings, Swansea had instantly impressed. Their eventual evisceration cannot mask the excellence of their first-half display.

Brimming with pace and belief, Brendan Rodgers’s wingers had been first to show. Scott Sinclair started running at Micah Richards and then Nathan Dyer raided down the right, lifting in a cross that would have reached Danny Graham but for the head of Vincent Kompany.

Mancini looks for much of his width from his full-backs and Gaël Clichy began gliding down the left. Richards, typically buccaneering, motored down the right, although not neglecting his defensive duties. One tackle on Sinclair was a particular gem.

For 20 minutes, City seemed to be paying too much respect to Swansea. Mancini’s men sat too deep, almost inviting their guests into their half. Leon Britton, a pedigree terrier in midfield, enjoyed a magnificent half, refusing to be daunted by the size or reputation of Yaya Touré.

Swansea’s keeper, Michel Vorm, was not far behind Britton in importance, making some vital saves.

City began to raise their game, pushing on, getting Silva more on the ball. The little Spaniard was instrumental in much that was finally good about City. Collecting a short corner from Johnson, Silva played a one-two with Nigel de Jong before unleashing a powerful shot that Vorm acrobatically pushed away. City fans sighed in frustration. Swansea’s fans simply redoubled their noise.

On came City again, Dzeko doing well to find Yaya Touré. Johnson took the move on, squaring to Silva, whose first-time effort hit Vorm’s bar. Again, City’s supporters shook their heads. Dzeko, initially poor, began showing signs of life, dispossessing Ashley Williams and drilling in a low cross that Britton cleared.

Still a light blue wave rolled towards Swansea’s goal. Vorm denied Yaya Touré and then thwarted Dzeko, who had just dragged the ball around Steven Caulker. City seemed to be getting closer and closer. Gareth Barry struck the crossbar as the hosts swarmed forward.

City intensified their efforts after the break. Yaya Touré shot wide and then the muscular Ivorian charged in from the right only for Vorm to clutch his cross. Swansea still counter-attacked, and Stephen Dobbie demanded a good save from Joe Hart.

But then came Dzeko, calming local nerves. Silva, inevitably, was at the heart of the move that led to City’s 57th-minute goal. Spotting Johnson’s run, Silva picked out the Englishman, who cut inside and unleashed a shot that Vorm palmed away. Mistakes get punished at this level and Dzeko, delighted by the gift, rolled the ball into the empty net.

As if to remind Swansea of the gulf in financial class, City then introduced Agüero, who almost scored with his first touch. There is a gunslinger’s swagger to the Argentine, a palpable belief in his own ability, that should sharpen City’s cutting edge.

He soon scored, within eight minutes of coming on, timing his run perfectly towards the far-post to turn in Richards’ cross. Agüero had not finished, hooking the ball across, albeit after it had probably crossed the line, for Silva to make it 3-0.

Agüero continued to command the attention. His touch and calmness in the box continued to alarm Swansea. He even flicked a pass to Yaya Touré who failed to exploit the chance. No matter. Agüero went himself the next time, sending a right-footed 25-yarder dipping past Vorm.

What a goal. What a signing. City are up and running.