It was little wonder during this tensely unpredictable encounter that the managers' stress-ometers were stuck at dangerous levels. Arsène Wenger lurched from the agony of watching his team start with the smoothness of the three-wheeler belonging to Trotters Independent Traders, via the exasperation provoked by refereeing decisions, to the desperation of willing his players to turn second-half pressure into goals. Meanwhile, Rafael Benítez's early comfort deserted him as he spent the latter part of the game dancing jerkily around his technical area. His expression was extremely harassed.

Chelsea feared the worst in the second half. That seemed barely imaginable during an opening spell in which they swarmed over Arsenal. Juan Mata was the virtuoso. His hooked shot to open the scoring was technically perfect. Oscar and Eden Hazard supported with runs that threatened to squeeze the life out of the opposition. Ramires strode around like a giant. Frank Lampard grafted, scored a penalty with customary ease and made you think Ashley Cole was not the only one who should have a new deal signed any day now. Everything in the Chelsea garden was rosier than it has been in these parts since they thumped eight goals past Aston Villa.

The sudden drop in performance level was so stark, as Arsenal were handed an over-generous invitation to help themselves, virtually any story line could have played out. Theo Walcott began to terrorise Chelsea and his team-mates surged forwards in search of more.

Forget the snow – a compelling reason why a winter break would be worth considering in English football was evident on the pitch at Stamford Bridge. These are two teams with maddening inconsistency. Two sides capable of producing bewitching moves for one half of a game, and bewildering in the other. This feeling of instability can affect just about everyone. It was there last weekend when Manchester United overpowered a limp Liverpool for the first 45 minutes, then the boots were switched on to the other feet during a nervy climax.

Both Chelsea and Arsenal are finding it tough to find regularity in their performances. Is it fatigue? Is it psychological? Even the managers struggle to give a clear explanation. But it is hard to see how a breather would not at least give every-one a chance to take stock and recharge.

It is hard to look for consistency over a period of games when it cannot easily be managed over 90 minutes. The guttural roars of relief as the final whistle confirmed a home win for Chelsea were meaningful because recent events bred little confidence of happy endings. Memories of the defeats to QPR, Swansea, and the couple of points that slipped through the fingers against Southampton, were fresh.

Chelsea can take heart from seeing this one out. Benítez had acknowledged the need for more character, for some players to take control and stay calm when the pressure rises, and it came from an unlikely source.

Gary Cahill is an understated sort. He is not by nature a shouter, an organiser, a leader. But his performance was exemplary. He won header after header against Olivier Giroud, and was responsible for a match-winning clearance in stoppage time. Come full-time, he reached out to high five his central defensive partner, Branislav Ivanovic, then peeled off his shirt to throw it into the crowd.

For the interim coach, emerging unscathed from a home match - and notably there was very little evidence of anti-Benitez sentiment from the Stamford Bridge crowd - was reason enough to be perfectly satisfied.

Wenger looked deflated at the end. Although he was disappointed with some early decisions, he was not exactly indignant. While dismayed with the Ramires foul that started the move for Chelsea's opener, he rightly pointed out Arsenal could have defended better from that point. Unsurprisingly, he was not exactly thrilled about the penalty.

But you sensed he was mostly concerned that his team, for the second time in succession, had built themselves a mountain to climb with a meek, anxious attitude at the start. They ceded the initiative from kick-off, as they did against Manchester City. These false starts are costly. This issue cannot be fudged for much longer.

Defending with the authority of disorientated tuk-tuk drivers faced with flying cars coming in the opposite direction is not a promising way to begin a football match.

It was telling that as they tried to claw their way back into the game, Wenger found himself throwing Andrey Arshavin into the fray. A player he has metaphorically put out to grass for the last year and a half, the Russian's touch was heavy enough he may as well have worn snow boots.

Chelsea might still have some problems to iron out, but thanks to a welcome three points, they could thaw out with a smile on their faces.