By the time Sergio Agüero was finished it was difficult to imagine quite where he finds the space to keep all the balls he has collected as souvenirs of his hat-tricks.

Agüero, one imagines, can afford the kind of property where they are all on show, along with enough trophies and medals to fill an aircraft hangar. Which is probably just as well bearing in mind this was the 14th time he has scored three or more in a game for Manchester City. Ten of those hat-tricks have come in the Premier League and, if you were to believe that top-division football was invented in 1992, the relevant statistic is that only Alan Shearer, with 11, has more.

Who would bet against Agüero claiming that record for himself one day? His priority, of course, is another championship medal but, on this evidence, maybe he would like to think the two even go in tandem.

Manchester City v Arsenal: Premier League – live! Read more

These were the goals that meant him reaching the 20-goal mark this season, as he has done in seven of his eight years in Manchester, and when his latest hat-trick was confirmed – a little fortuitously bearing in mind the ball went in via his ribs and elbow – it meant he had scored 22 times during the last 15 home matches for City when he has been in Pep Guardiola’s starting lineup.

More importantly for City, he had also made the telling contribution on the day the reigning champions gave Arsenal a harsh reminder about the level of artistry that is required to harbour authentic title aspirations.

For Arsenal it has been a long time since they held that information for themselves and they have fallen to sixth position. City, in contrast, have moved within two points of Liverpool. They have scored at least twice in every home match this season and would dearly appreciate a favour from West Ham when the leaders play in London on Monday.

Agüero’s performance, comprising the 217th, 218th and 219th goals of his City career, certainly warranted the crowd’s acclaim when Guardiola replaced him with Gabriel Jesus at the 80-minute mark.

The Argentinian had scored after only 24 seconds in City’s previous game at Newcastle. This time his first one was timed at 46 seconds and, unlike the trip to St James’ Park, there could be no accusation of City’s players looking bored with their own brilliance – or the word that every elite manager despises: complacency.

Manchester City v Arsenal: player ratings | Jamie Jackson Read more

The visitors did toy with the idea of making a fist of it after Laurent Koscielny had surprised everyone, perhaps even Arsenal themselves, by scoring with an 11th-minute header. Unai Emery and his players were aggrieved that Agüero’s hat-trick goal was not ruled out for handball. Yet they will also know it could well have been a more emphatic victory for City on the balance of play. Agüero had restored City’s lead late in the first half and the home side’s domination after the break was a reminder that Liverpool will have to play exceptionally well to shake them off between now and May. In the second half City managed 13 attempts at goal, Arsenal zero.

Not that this was a lopsided display from the winning team. Right from the start City seemed intent on getting the defeat at Newcastle out of their system. Guardiola’s side love to take early control, to worry their opponents from the first whistle, and it resulted here in one of their defenders, Aymeric Laporte, venturing forward to dispossess Alex Iwobi on the edge of Arsenal’s penalty area and set up the opening goal. Agüero, alert as ever, was waiting for the cross, twisting his body to direct a stooping header past Bernd Leno, the goalkeeper.

Facebook Twitter Pinterest Agüero looks on as the ball trickles over the line for his third goal. Photograph: Stu Forster/Getty Images

For a while it looked as though Arsenal would be overwhelmed by the sheer ferocity of City’s early pressure. All of which made it surprising, to say the least, when the away team emerged from the onslaught to equalise. Lucas Torreira whipped a corner over, Nacho Monreal won the first header and Koscielny had broken away from Raheem Sterling – a strange choice of marker – to score with the next one.

The corner, the flick-on and the back-post finish – and, for City, the slightly worrying statistic that exactly half of the 20 goals they have conceded in the league this season have come from set plays. It is the highest percentage in the top division and something, presumably, that not just Emery will have noted among opposition managers.

For Guardiola a little insecurity at the back is the downside, perhaps, of being so attack-minded – they set up here with Fernandinho operating as both a midfielder and auxiliary centre-half. When City were going forward, Laporte and Kyle Walker both had carte blanche to break out of defence and spread play by moving wide and morphing into attacking full-backs.

Nicolás Otamendi was sometimes the only player left back, with Fernandinho drifting between his two positions and often joining Ilkay Gündogan in midfield. Ahead of them, Kevin De Bruyne and David Silva had Sterling and Bernardo Silva operating either side of Agüero. It was a formidable lineup, albeit one that occasionally threatened to leave City open to the counterattack.

The Fiver: sign up and get our daily football email.

For that to happen, however, Arsenal needed to get the ball first. Agüero’s second goal came from close range after a lovely exchange of passes involving Sterling and Gündogan and the striker dived in to complete his hat-trick just after the hour.

Again it was Sterling playing the decisive pass across the six-yard area. Arsenal’s players gathered round the referee, Martin Atkinson, to protest that it was handball but Agüero was already wheeling away, with that familiar smile, the arm raised and the guarantee of another ball for his personal collection.