Midway through the second half of Manchester City's controlled, clinical and ultimately rather sedate 2-0 victory at the Emirates the travelling supporters could be heard chanting "£62 but we're still here" – and much was made in the build-up to this match of the steepling ticket prices that led to 900 away tickets remaining unsold, even for a match that had, as ever, assumed a quietly pivotal importance for both club's Premier League ambitions.

True to football's own innate gallows sense of humour, the £62 match was in the event pretty much over after eight minutes. Laurent Koscielny's sending-off for a full-body embrace of Edin Dzeko – preventing an opportunity to shoot at goal from six yards – was a blow Arsenal were never likely to recover from. If Arsène Wenger was later rather more magnanimous, his instant reaction was predictably fraught, stalking his technical area with arms splayed and quilted gown furiously swished, furious not with his defender for committing a clumsy foul but with the referee for a correct but rather unforgiving application of the rules. The Emirates crowd erupted too and later rose as one to boo the referee Mike Dean and his assistants from the pitch.

There is a sense of necessary theatre in such a reaction but in practice this was a correct decision where the only shades of grey were vague appeals to a broader clemency. Defensive grappling: everybody does it but by the same token everybody also wants it to stop. A yellow card might also have saved the game from being ruined as a spectacle. But so close to goal it was plainly a red-card offence, albeit one born out of habit and instinct rather than malevolence.

By the time Vincent Kompany was sent off with 14 minutes remaining the match had been decided by two moments of incision from City and some answering defensive slackness. It should be noted Kompany's sending-off was a similar case: not an outrageously bad tackle on Jack Wilshere but a lunge with enough excessive force – the key ingredient – to make it a dangerous challenge. Again the offender had plenty of complaints, as did Roberto Mancini afterwards, enraged at losing his captain to suspension. City will appeal.

If there was initially hope for Arsenal here, it sprang from Dzeko's missed penalty, Wojciech Szczesny producing a quiz question of a save, diving completely the wrong way but still somehow ending up clawing the ball off the line after a favourably zany rebound off the post. There was some entertainment there perhaps for the £62 punter as briefly the match remained in the balance, but not for long. The first goal was soft but also brilliantly severe in execution, the product of an utterly distracted attempt to construct a defensive wall, Arsenal's defenders milling around while two City players touched the ball unopposed to tee up James Milner. His finish from an angle was sublime, the ball smashed high inside Szczesny's far post.

Milner it was who played the major hand in City's second after 31 minutes, his low cross from the right ending up with Dzeko tapping home. But it was Pablo Zabaleta's persistence that made it possible, the Argentinian walking through Kieran Gibbs' attempted challenge with embarrassing ease on the left touchline and feeding David Silva. For City a potentially tricky afternoon at a ground where they had not won in 37 years had been transformed into a stroll, to the delight of the travelling support, less so those Arsenal fans who took up the remaindered £62 hot tickets as part of another 60,000 full house.

Dzeko, City's attacking focal point here, held the ball expertly and showed some wonderful movement, combining well with Carlos Tevez, who was allowed to roam imaginatively as a second striker. Milner, too, had a fine match. The second most expensive English footballer of all time has been in and out of the City side but the absence of key players for the next month offers an opportunity to reassert his understated virtues. If City had cause for concern, it is in their failure truly to put Arsenal away after half-time, but this is to underplay Arsenal's own spirit, with Wilshere once again producing his better form against better opponents.

Beyond this, and even in a match effectively decided by Koscielny's red card, there was enough evidence again here of the armature of a callow but enterprising Arsenal team that begs the question of what might have been had they managed not just to retain their best players but to recruit more aggressively. It is increasingly Arsenal's lot to ponder the parallel exploits of the shadow team that got away and, while only Gaël Clichy in City's team on Sunday arrived directly from the Emirates, in recent years Arsenal have made attempts of some kind to sign all four of City's starting midfielders: most recently Javi García, who was resolute in the centre. The £62 match ended with City seven points behind Manchester United in the Premier League but also looking like a team with strength in reserve. No doubt their travelling fans will settle for that.