Chelsea have spluttered amid the poisonous atmosphere allowed to fester in this stadium over recent weeks but Arsenal's visit provided an antidote of sorts. All that rancour was forgotten amid the distraction of a rumbustious derby, the dissent at Rafael Benítez's mere presence more a grumbling than bellowed protest. Victory against local rivals has strengthened Chelsea's position in third. Any respite is to be cherished.

This being a Chelsea side engulfed in a season of tumult, there was still the fluttering of nerves to suffer through a second half when the visitors, so dishevelled up to then, revived and rallied. Benítez's side clung on desperately at times but where they had wilted against Queens Park Rangers, Swansea City and Southampton, their resistance endured for once. Gary Cahill stretched out a seemingly telescopic limb to deny Theo Walcott in the six-yard box almost four minutes into stoppage time, and Olivier Giroud looped a header on to the roof of the net seconds later. The final whistle was celebrated with gusto.

It felt rare for Chelsea to have cause for celebration in these parts. Refreshing, even. This was only a second home win in the seven domestic fixtures overseen by the interim manager and timely in deflating Arsenal's aspirations to remain regulars in the top four.

The sense of normality being restored stretched even to the 16th-minute tribute to Roberto Di Matteo going forgotten, if only because the locals were too busy anticipating and then celebrating Frank Lampard's 195th goal for the club, converted from the penalty spot, at the time. Throw in the welcome news that Ashley Cole has agreed a contract extension through to 2014 and this all felt unusually upbeat. Roman Abramovich even managed a smile at the end. So much for doom and gloom.

Inevitably, it is too simplistic to suppose this is the turning of the tide. There is too much vulnerability to Chelsea to assume they will travel to Swansea on Wednesday and run riot to overturn the two-goal deficit surrendered in the first leg of their Capital One Cup semi-final. Benítez could win that competition, the Europa League and FA Cup, and qualify for the Champions League, but still be dogged by abuse in this stadium.

Yet, at their attacking best, Chelsea are still a force and had swarmed all over disorganised opponents – Eden Hazard, Oscar and Juan Mata leaving Arsenal dizzy. It was a reflection of their psychological fragility that they permitted the visitors to dominate after the interval but both these sides are afflicted by inconsistency. On this occasion, Chelsea did enough during their own period of ascendancy to squeeze home.

Both the goals they scored were controversial. Ramires, an explosion of energy throughout, stepped on Francis Coquelin's foot just inside the Chelsea half for the first, César Azpilicueta springing on to the loose ball to free Mata as the Frenchman sank to the turf in pain. That was cause for complaint, though Bacary Sagna was still the wrong side of Mata as he burst through to finish. "It's frustrating but it doesn't mean we should have conceded the goal," Wenger said.

He could feel similarly aggrieved at the quarter-hour mark, both at his team's attempt at defence and with the officials' interpretation of events. Ramires dispossessed Abou Diaby too easily to send Mata into enemy territory, with the Brazilian then allowed to charge unchecked to collect the return alone inside the area. There was an attempt to edge round Wojciech Szczesny but, as the chance threatened to veer away, out came a foot to ensure contact with the goalkeeper and a tumble to the floor. Lampard duly scored from the spot and Chelsea were back where they had been in midweek against Southampton, two goals up and apparently comfortable.

Yet, as Rickie Lambert had proved then, all it takes to discomfort them is some urgency from the opposition and a hint of retreat. Arsenal pressed higher upon the resumption, their own conviction growing despite Per Mertesacker, Giroud and Walcott all being denied by Petr Cech. Benítez sensed what was coming, barking orders almost indiscriminately from his technical area and pleading for concentration, but minds were frazzled. Santi Cazorla, peripheral up to then, duly squeezed a fine pass behind a back-tracking Branislav Ivanovic for Walcott to collect and finish smartly.

How Wenger must curse his team's inability to start contests with that much intensity. As they poured at their hosts, pinning them back, Arsenal looked like contenders with Walcott, in particular, discomforting Cole as he has so often with his jet-heeled darts.

Admittedly, they gambled and were left open at times on the break, not least when Demba Ba was able to amble forward alone and round Szczesny only for Thomas Vermaelen to scramble his shot from the goalline. But had they started with as much attacking zest as they finished then it might have been Chelsea who shrunk.

As it was the home support roared their approval for Cahill's late intervention, the England defender taking on the John Terry role while the club captain shivered unused on the bench. It has needed a last-ditch tackle like that to get the blood pumping, a glimpse of strength to remind this team what their qualities used to be. Benítez will believe he can build on this win, not least at the Liberty Stadium on Wednesday, with third place consolidated. For Wenger, with similar problems flaring too regularly, the top four feels distant yet again.

Man of the match Ramires (Chelsea)