This curiosity of a contest said everything about these two teams’ current travails. It pitted one in serious crisis – Everton – against one always seemingly near to the next – Arsenal. An odd sense of elite professionals muddling through prevailed until Idrissa Gueye was sent off on 68 minutes and the Gunners pulled away.

Before then Everton and Arsenal had each suffered from an absence of stability and clearness of vision. Instead the players lurched from one disjointed moment to the next. The Gunners began like the proverbial train that suggested a seventh defeat in 11 matches would be Everton’s fate. Then they did an “Arsenal” by allowing their confidence-low opposition to take the lead, via a fine Wayne Rooney strike.

Until then the game had been a microcosm of Everton’s ills. Ronald Koeman’s men were second to 50-50s, sluggish to pick up runners and too open. One move should have ended with Aaron Ramsey firing Arsenal ahead, another might have seen Michael Keane conceding a penalty for chopping at Alexis Sánchez.

Jordan Pickford’s reflexes kept Everton level more than once in an uncertain, chaotic start which was reflected in a formation difficult to fathom: was it 3-5-1-1, 3-3-3-1, 5-3-1-1 or something else Koeman sent out?

There was, though, only decisiveness in the way Everton took the lead. Gueye steamrollered the suspect Granit Xhaka to take the ball. He would later receive his second yellow card for a clumsy effort on the same player. This time, though, he fed Rooney and his curled shot gave Petr Cech no chance.

For Arsenal to be mugged by this Everton outfit was the latest evidence of the deep faultlines in Arsène Wenger’s team. Even by the Frenchman’s standards Xhaka’s continued selection is a curiosity. Central midfield is the defining area of every match, the zone where the dominant force usually dictates outcome. To earn a starter’s jersey there the base requirements are a cool-eyed first touch and high-end spatial awareness: Xhaka’s mistake shone a glaring light on his deficiencies in these departments. Sead Kolasinac is another odd Wenger choice: the 24-year-old may be a cult hero to fans but his rudimentary abilities for the left wing-back role says much about why Arsenal can be so disjointed.

After the goal the sides’ discordant struggles continued. Everton got at their opponents for the odd passage before they were pinned back and dominated again. “Arsenal-itis”, that affliction of having to score the perfect way, caused Mesut Özil, Ramsey, Alexandre Lacazette and Héctor Bellerín all to falter on entering the danger zone near Pickford.

When they did equalise it was both deserved and slightly jarring, given their previous inability to convert ball possession ascendancy into material reward. So, when Xhaka’s 30-yard shot appeared speculative it was apt that his team equalised via a mistake: Pickford spilled and Nacho Monreal did the rest from close range.

By the break the sides were in a state of flux. Now was the time for Koeman and Wenger to earn their corn by making adjustments that would help their sides. Koeman brought on a forward-thinking player, Tom Davies, for a defender, Ashley Williams. Everton had a four-man defence and were now a 4-2-3-1.

Did it work? Well, possibly until the match’s uneven nature confounded again. Rooney, Jonjoe Kenny and Dominic Calvert-Lewin all offered bright moments before disaster struck for Everton with the kind of sucker-punch managers detest. Arsenal broke quickly via Lacazette, Ramsey and Sánchez who, from the left pinged the ball on to Özil’s head and he flicked it past Pickford.

At once the travelling Arsenal fans regaled Koeman with: “You’re getting sacked in the morning.” Whether going behind provoked the owner, Farhad Moshiri, who was present, to consider this is unclear. But what followed will not have boosted his mood or Koeman’s long-term job prospects. First, Gueye’s second yellow card reduced Everton to 10 men. Second, Lacazette beat Pickford and Koeman was staring at a 3-1 deficit which by the close was 5-2 as Ramsey’s and Sánchez’s later finishes sandwiched Oumar Niasse’s.

The sense beforehand was that Moshiri and the board would give their manager more leeway. They concede a failure to buy Olivier Giroud or AN Other as Romelu Lukaku’s replacement to fill the void at No9 was a big mistake. But, really, Koeman should have pushed more for a centre-forward in the summer window. Instead he settled for Rooney, Gylfi Sigurdsson and Davy Klaassen, all natural No10s.

This baffling recruitment process sums up the issues for Everton and Koeman. The Dutchman wants more time. How much more he will receive is the question.