Rafa Benitez's team moved 11 points clear of its rival for a Champions League place following an excellent first-half display in the snow.
Early goals from Juan Mata and Frank Lampard put the home side in complete control but Theo Walcott’s brilliant 58thminute strike gave Arsene Wenger’s team hope.
However, with the snow tumbling down, Chelsea was able to avoid a repeat of the midweek fixture here against Southampton by not letting slip a two-goal lead.
It enabled Rafael Benitez’s team to take a firm grip on third place and establish clear distance between itself and Arsenal, which limped to its second consecutive league defeat after losing to Manchester City last weekend.
Wenger’s side showed heart and fight to make a game of it in the second half but was ultimately made to pay for a feeble first-half showing in which the team was comprehensively out played and out thought by the home side.
Chelsea was so fluent and dominant in the early exchanges that the home support forgot to continue the 16th-minute tradition of chanting the name of Benitez’s predecessor Roberto Di Matteo.
It was enough to leave those who did not take up their seats because of the snow that tumbled down in west London all day and throughout the match kicking themselves with envy.
With Lukas Podolski missing through illness, Arsenal selected the same XI that dumped Swansea City out of the FA Cup in midweek, with Olivier Giroud spearheading the attack and Theo Walcott starting on the right.
Chelsea made two changes from the side that drew at home against Southampton. Branislav Ivanovic, who was on the bench on Wednesday, replaced the injured David Luiz and Fernando Torres came in for Demba Ba.
Early on, Giroud wasted a great opportunity to put Arsenal ahead after being put through by Walcott, and Chelsea immediately made the visitors pay for the let off.
The home side broke up the field where Cesar Azpilicueta delivered an excellent cross-field pass to Juan Mata, who pulled the ball down with a wonderful first touch and hammered it into the net with his second.
After 15 minutes, the visitors were sliced open once again after Abou DIaby was robbed of the ball in the middle of the park. Mata found Ramires in acres of space in the penalty box and the Brazilian dawdled before falling over Szczesny’s outstretched leg and Chelsea was awarded its eighth spot kick of the season.
Szczesny, who had cover from his defenders, escaped with a yellow card but could not prevent Lampard converting the 47th penalty of his Chelsea career.
From then on, it was one-way traffic throughout the opening period. Arsenal’s frustration was encapsulated by an animated Jack Wilshere, who, isolated in an advanced attacking midfield role, could not get the ball and made no attempt to hide his disgust at his teammates’ failure to treat their passing with care.
Arsenal was much improved after the break, creating three good opportunities before Walcott sprung the Chelsea offside trap after 58 minutes.
Santi Cazorla threaded the ball through to Walcott, who opened up his body to fire it magnificently past the grasp of Petr Cech to give his team a life line.
With Wilshere increasingly influential and Walcott a constant threat on the right, Arsenal looked the better team. However, Wenger made his feelings clear about the effectiveness of his central midfield by subbing both Coquelin and Diaby.
Despite their late rally, Arsenal could not find a way through a Chelsea defense that was far more resilient than it had been against Southampton on Wednesday.