Manchester City are off and running and, in the process, the seemingly ceaseless issues surrounding Carlos Tevez no longer seem quite so important. Roberto Mancini's team were rampant throughout the second half and, as debuts go, it is difficult to think Sergio Agüero could have done much more to ingratiate himself with his new supporters.

Agüero was introduced shortly after Edin Dzeko had opened the scoring against a Swansea City side who outpassed their opponents for the first 30 minutes before fading badly. Within nine minutes of coming on he had made it 2-0. Still not satisfied, he then created the third for David Silva but it was the moment when he made it 4-0, with full time approaching, that he fully announced his arrival in English football.

Agüero's second goal of the night was struck from 30 yards: a swerving, dipping, brutal shot that speared into the net. The Etihad Stadium has a new hero and, if he continues like this, maybe Mancini's team may yet score the "10 to 15 extra goals" he believes will turn them from Champions League qualifiers last season to a side with realistic aspirations of winning the league.

Mancini eulogised about the £38m signing, reflecting on a "perfect night" that began with City's players warming up in T-shirts bearing the slogan "I Love Manchester." Tevez, in Manchester against his will and off-message for longer than the club will care to remember, was nowhere to be seen. True to form, the club captain – and it is surely only correct that title is removed from him for good – was not even in the stands but this did not feel like a night for recriminations. "I'm not surprised by what I saw tonight," Mancini said. "Agüero has scored a lot of goals in Spain and Argentina – he's a fantastic striker."

By the end, Swansea were grateful to hear the whistle. They had some good spells and can be encouraged by the way they dominated the opening exchanges. Yet, for all their neat and attractive football, they were seldom a genuine threat and Joe Hart made only one noteworthy save all night.

Brendan Rodgers has assembled a side who are capable of keeping the ball under pressure and they will win many admirers but he may yet have to impress on his team that, when they are on top, it is crucial in this league that they make it count.

Instead Mancini's team recovered from a difficult start and, by the closing stages of the first half, Swansea's goal was being subjected to concerted pressure. Silva, almost inevitably, was prominently involved. One diagonal shot brought a splendid flying save from Michel Vorm. Another effort from the Spaniard struck the crossbar. Dzeko looked busy, sharper than he was last season, and was also identified by Mancini for special acclaim. Adam Johnson, chosen ahead of Mario Balotelli, worried the Swansea defence. Yaya Touré found his passing range after struggling early on.

Vorm, a £1.5m signing from FC Utrecht, had an inspired 15-minute period when he kept out everything and Swansea had a bit of luck, too. When Gareth Barry slashed a left-foot effort through a congested area the crossbar shook for a second time but Swansea had lost their early verve and it was no surprise when Dzeko began the rout.

Silva started the move, wriggling away from Leon Britton inside his own half and advancing through the middle. His pass sent Johnson scampering clear, cutting inside from the right before trying to curl a shot past Vorm. The Dutchman got both hands to the ball but turned it straight into Dzeko's path, six yards out for a relatively simple finish.

The match would soon turn into an ordeal for the team embarking on their first top-flight season since 1983. Agüero's debut goal was a simple tap-in at the far post after Micah Richards had sent over a low cross from the right.

Three minutes later Dzeko's pass sent Agüero clear. The Argentinian lifted the ball over the oncoming Vorm and adjusted his body to hook it back from the byline. Silva was waiting on the penalty spot to stroke his shot into an exposed goal.

And then the special moment. Agüero's second goal was unstoppable – "world-class from a world-class player," as Rodgers said – and, in that moment, we had the confirmation that the club of Abu Dhabi wealth and ambition had ushered a new superstar into the Premier League. Carlos who?