Arsène Wenger's 1,000th game will always be remembered for The Mysterious Case of the Wrong Red Card, but Arsenal should probably be grateful the sideshow was so intrusively farcical, and the refereeing so birdbrained, it might spare them even greater scrutiny. Ignore, for one moment, Andre Marriner's contribution to a wild and eccentric afternoon. The real story was of Arsenal capitulating, once again, in one of the fixtures that identify champions.

Add this to the 6-3 ordeal at Manchester City and the 5-1 at Liverpool and there is a clear pattern to explain why Wenger will not be collecting the Premier League trophy to go alongside that gold cannon he has just received for his long service. The aggregate score is 17-4 and Wenger's mood could probably be summed up by his decision, for the first time in his 17 and a half years in charge, not to face the post-match press conference.

His team had played with no comprehension of what it takes to hold Chelsea and they suffered badly for it. They were 2-0 down inside the opening seven minutes. Two more arrived before half-time and, by the end, it was not just José Mourinho's biggest ever win in control of Chelsea but the heaviest defeat Arsenal have suffered in 107 years of this fixture. Wenger has not beaten Mourinho in 11 attempts and the indignities piled up. At one point, Chelsea's jubilant supporters could be heard chanting for him to sign a new contract: "We want you to stay". Later, an even more callous cry went up: "Specialist in failure".

Chelsea can hardly have believed the gifts that were presented to them, neatly wrapped in red and white ribbons. Mourinho's team played with common sense and title-winning know-how. They were ruthless in attack, controlled in midfield and untroubled in defence. Everything that was missing from their opponents.

Arsenal's carelessness was both damaging and extreme. They were a rabble and, at this level, a team cannot expect to get away with these kind of collective failures.

The tone was set in the fifth minute when Alex Oxlade-Chamberlain lost the ball in midfield and Chelsea swept upfield to score through Samuel Eto'o. Three minutes later it was Santi Cazorla's turn to give the ball to Nemanja Matic and, again, the home team's swift, penetrative counterattacking resulted in a goal, this time through André Schürrle.

Lest it be forgotten, it is not just Marriner who should reflect on Kieran Gibbs's bizarre and unwarranted dismissal with intense embarrassment. Marriner messed up badly and it will be a long time before he lives it down but, from Arsenal's perspective, there was no need in the first place for Oxlade‑Chamberlain to stick out an arm and turn away Eden Hazard's shot. The ball was going at least a foot wide, without any need for a midfielder to double up as an emergency goalkeeper. It typified the decision-making of Wenger's players.

That passage will leave Wenger's party-cum-nightmare with a certain infamy and there really is little excuse for Marriner bearing in mind Oxlade-Chamberlain clearly could be seen owning up that it was him. By then, Marriner had shown a red card to Gibbs. The referee's reaction – ignoring what Oxlade-Chamberlain was telling him, Gibbs's protests and the general shock of everyone around him – was haughty and self-defeating. The Premier League is sure to act, correcting the decision, and it is surely time for fourth officials to have access to a television monitor.

As soon as Hazard tucked in the penalty, it was obvious there was no way back for Arsenal. Even so, they should surely have done a better job at sparing themselves more embarrassment. Fernando Torres, a substitute after Eto'o's hamstring injury, surged down the right and crossed for Oscar to make it 4-0 and, after that, it was almost a surprise Chelsea restricted themselves to only two more.

As Wenger sent out a club spokesman to say he had already boarded the coach, Mourinho could be found reflecting on the first "10 amazing minutes", expressing faux outrage that 2-0 after seven minutes could not become "20-0 after 70 minutes".

No matter. This was also the day Mourinho was prepared to admit his team had gone from having "no chance" of the title to "just a little". Yet the awkward truth for Wenger is that no other opponent will be this obliging.

For the fifth goal, Tomas Rosicky played a wayward pass from the right-back position and Oscar simply took the ball and stuck a right-foot shot past the unimpressive dive of Wojciech Szczesny. Within four minutes, Matic's through ball had split open the entire Arsenal defence for Mohamed Salah to run clear. Salah had been on the pitch four minutes and confidently slipped a low shot past Arsenal's goalkeeper.

Matic had also been prominently involved in the first two goals. For the first, Eto'o checked back on his left foot and curled his shot into the far corner. Schürrle angled in a precise shot for the second and, after that, the day went from bad to worse for Wenger, Arsenal and a referee who probably feels as embarrassed as anyone.