Welcome to the Premier League then, Manuel Pellegrini. And can we please have a little more of this. In the course of a slow-burn start to the season there are those who may have mistaken Manchester City's quietly revered Chilean manager for a courteous and rather benignly intentioned South American technocrat. If so it is hard to imagine a more decisive moment of personal ignition than this: not just a 4-1 defeat of the champions but at times a complete footballing destruction.

To date in England Pellegrini has been a soft-pedalled, rather gentle presence, positioning himself outside the familiar operetta of duelling soundbites, and focusing instead on trying to wring the best out of City's early season combinations. There was nothing gentle about this though, as City produced a performance of ruthless speed and movement and of chasteningly superior midfield power.

"I've had plenty of moments like this at Everton," David Moyes said afterwards. This, though, isn't Everton. The 6-1 defeat at Old Trafford two years ago was a more ragged affair, but is hard to remember a more complete, almost rather cruelly playful performance against a Manchester United team.

Most worryingly for Moyes, deprived of Robin van Persie and with his team arranged in a distinctly linear version of 4-4-2, there was a sense of something drab and retrograde about the scope of United's ambition. At times, as Wayne Rooney scampered about the pitch in pursuit not just of the ball but of a team-mate willing to take it with any confidence or dynamism, it was a bit like watching Roy Hodgson's England in one of their more tortured moments.

Really though, this was all about Pellegrini's City. United were outplayed, but first they were out-muscled. Perhaps the lowest point of a wretched afternoon for Marouane Fellaini – not so much United's midfield policeman here as a rather meek and apologetic community support officer – came in the build-up to City's fourth goal. Finding himself in the slipstream of Jesús Navas, and with United's left flank vacated, Fellaini decide to try and catch up. It was a horrendous sight as Navas skipped away effortlessly with the ball, slowing down and speeding up like a cartoon mouse evading a broom-wielding middle-aged janitor, before laying on City's fourth goal for Samir Nasri.

Elsewhere City's superior muscle was most obvious in Yaya Touré's complete ownership of the middle of the pitch in the first hour. Before kick-off Fellaini versus Touré had seemed an alluring prospect. Here in the cagey opening moments they resembled of a pair of medieval siege engines being wheeled into close proximity, circling warily, hinges clunking.

Before long, though, United's headline summer signing was being cut out of the game far too easily by the passing angles and nimble-footed movement of City's over-manned midfield. Carrick and Fellaini does not look a well-balanced central duo. But then Touré when he stirs himself fully can be irresistible, a wonderful combination of vast galloping thighs and neat and purposeful touches. His goal, City's second, came from a corner that saw Touré run off the back of Fellaini to bundle the ball home off his spring-loaded knee.

For all its obvious physicality only the most deluded optimist could describe this as an English performance from a Pellegrini team with no English outfield players in its starting XI. There was a degree of zip and strength English teams might aspire to. But this might be characterised better as an Argentinian performance, with hard, intelligent running combined with expert manipulation of the ball in midfield and attack, and Aleksandar Kolarov at times transformed into a left-sided Javier Zanetti tribute act.

"We are just starting another style of play," Pellegrini shrugged afterwards, but in City's game of sprints there was a glimpse of pieces slotting into place, and of lessons eagerly leant.

There were more specific victories for Pellegrini, most notably in his choice of strikers. Here he began with Sergio Agüero and Alvaro Negredo for the first time, with both positioned right up against United's veteran centre-backs. It worked brilliantly, the combination of Agüero's acceleration and Negredo's power – nickname: the Beast of Vallecas – was horribly traumatising throughout the first half. Agüero in particular was magnificent here, scoring the first goal with a gymnastic, twisting finish from Kolarov's untracked run and cross.

What about United? They were very poor for an hour, let down most noticeably by a lack of zip and precision in their passing, and by a system, with Valencia and Ashley Young very wide, that left them looking at times as though they simply had fewer players on the pitch. There was some comfort in Rooney's energy and invention: an angry performance crowned with a superb free-kick goal.

Plus United do have other midfield options. In fairness to Moyes, this was a team sent out to stifle. Most alarming was the failure to respond when City refused to play with the caution Chelsea had shown at Old Trafford and instead seemed set on playing football from some alluringly high-grade version of the near footballing future. Pellegrini was gently magnanimous in victory, but his team had already spoken for him.