Arsenal 0 Chelsea 1

Arsenal have made a series of statements this season, as Arsène Wenger plods the long distance towards the ultimate vindication, such as beating both of the Manchester clubs at the Emirates Stadium and even getting a result at Stoke City. Some things, however, never seem to change.

Chelsea remain their nemesis, even without José Mourinho at their helm, winding them up and, well, beating them and it was another character who they have come to loathe that was the match-winner here.

Diego Costa was involved in a red card flashpoint – as he was in Chelsea's 2-0 win over Arsenal in September – but this time, there could be no recriminations. The striker was simply too fast for Per Mertesacker in the 18th minute and, when the Arsenal defender slid in and got none of the ball, there was an inevitability about his dismissal for a last-man foul.

Shortly afterwards, Costa showed the clinical side to his game in front of goal, when he pounced to meet Branislav Ivanovic's cross to fizz a shot beyond Petr Cech. It set Chelsea on their way to a sixth win over Arsenal in nine meetings (excluding the Community Shield); the other three have been drawn and, for Arsenal, the damage was severe.

All the focus and, indeed, the pressure had been on them, with Chelsea too good to go down and too far from the top four to make too much of the remainder of their league season. And so the global audience settled down to pass judgement on Arsenal’s championship credentials but they watched them fluff their lines.

Chelsea had settled the quicker and they created the clearest opportunity when it was 11 versus 11, with Willian denied by Cech at close quarters. Oscar had earlier worked the former Chelsea goalkeeper while Arsenal could point to a miscued volley from Joel Campbell and a half-chance for Mathieu Flamini. The midfielder, though, rather lunged at the ball, as though he were making one of his tackles, and the chance slipped away.

It was another tackle that shaped the game. Willian had blasted away from Aaron Ramsey on the counterattack and the moment that he released his pass for Costa, it was clear that Mertesacker was in trouble.

Mertesacker stretched into the challenge that he had to make but Costa was too quick and, in the blink of an eye, the Chelsea striker was rolling into a series of exaggerated rolls and everybody inside the stadium knew what was coming next. The referee, Mark Clattenburg, flashed the red card. He had no other option.

Costa set about salting the wound, and it took him five minutes to do so. Wenger had made the difficult decision to sacrifice Olivier Giroud for Gabriel Paulista – the replacement defender that he needed – and, if the Emirates crowd did not like the substitution, Giroud liked it even less.

The striker gestured with his outstretched arms and he dragged his heels, initially, as he made his way off, until Flamini came across to chivvy him along. Mertesacker and Giroud would be spotted in their club suits behind the Arsenal bench during the second half.

Gabriel versus Costa rekindled memories of the clash at Stamford Bridge from earlier in the season, in which the former had been sent off for a little dig at the latter. Gabriel was not up to the pace of the game when Ivanovic drove over his cross from the right and how Costa made him pay. Tip-toeing in front of him, Costa touched home his sixth goal in six games under Guus Hiddink, before pointing out the name on the back of his shirt to the Arsenal supporters closest to him.

Chelsea might have been further in front by the interval only for Cech to save from Costa at the near post and Nacho Monreal to clear off the line from Ivanovic’s header. And yet they could, equally, have been level. Following Ramsey’s smart dink over the top, Flamini – all alone 10 yards out – flew at the chance like Hong Kong Phooey out of a filing cabinet. To loud groans, he lifted his flying kick over the crossbar.

Chelsea's starting formation had broadly aped that of Arsenal but Cesc Fàbregas, in the No10 role, frequently dropped into deep areas to drive his team forward. The former Arsenal captain was jeered whenever he got on the ball but he let nothing bother him. He was outstanding, setting the tempo and impressing with his poise and vision. He felt that he ought to have had a penalty on 56 minutes when Laurent Koscielny checked him inside the area but Clattenburg was unmoved.

Costa played the pantomime villain to the last. He had gone down in need of treatment, to the scorn of the home support, when his number went up and Loïc Rémy prepared to replace him. Costa had the treatment, got up and walked off at low speed. When he approached the touchline, he had one final trick – applause for the Arsenal crowd – before he strolled off down the tunnel. This guy has some cojones.

Wenger played his trump card with the introduction of Alexis Sánchez on 57 minutes for his first football since 29 November and a hamstring tear, and the forward made a difference. Arsenal showed a bit of spirit in the second-half and both Nemanja Matic and John Mikel Obi were booked for fouls on Sanchez. Yet they did not seriously threaten the equaliser, with Sanchez's swing-and-miss following a scramble in the 63rd minute their best – and only – chance.

At full-time, several of Arsenal’s players slumped to the turf as Chelsea celebrated yet another victory over them. This one cut them to the core.

Man of the Match: Cesc Fabregas (Chelsea)

(Guardian service)