Juan Mata's excellent finish and a penalty from Frank Lampard gave Chelsea a two-goal lead after only 16 minutes as Arsenal's frail defence wilted under gentle but regular snowfall at Stamford Bridge.
The visitors couldn't help but improve in the second half and a 58th-minute goal by winger Theo Walcott — signed up on Friday for a further 3 1/2 years at the club — offered them hope of at least a draw.
Aided by some desperate defending, Chelsea hung on for only its third win in eight home matches — and first in four in all competitions — under interim manager Rafa Benitez. The European champions remain favourites to take the final automatic Champions League qualification spot behind the Manchester clubs, who are battling for the title.
"We are doing well and progressing," said Benitez, whose team's fast start meant he avoided the kind of crowd abuse that has marred his first two months at Chelsea.
Arsenal failed to recover from the damage inflicted by its dreadful first-half showing — arguably its worst 45 minutes of the season — and is now 11 points behind Chelsea. Finishing in the Champions League positions is far from guaranteed for Arsene Wenger's side, which has been a fixture in Europe's top competition for the past 15 years.
"The table is the table," Wenger said, bemoaning a second straight slow start following on from the 2-0 home loss to City last weekend. "We have lost two big games in the last week. That's damaging for us. We can't afford to lose more points. It's a concern."
Lacking leaders, defensively weak and failing to show the same work rate and hunger as its opponent, Arsenal was picked off time and again by Chelsea's effervescent midfield — led by Mata — in the first half. It should have been worse than 2-0 at halftime and Wenger had a face like thunder throughout the half.
"We only came into the game when we were 2-0 down — that's worrying," Wenger said.
Mata's goal came after Ramires escaped punishment for a foul on Francis Coquelin in the centre circle. While Arsenal's players protested, Cesar Azpilicueta lofted a ball over the visiting defence to Mata, who controlled expertly and fired a shot high into the net with Bacary Sagna trailing in his wake.
It was all Chelsea and Lampard made it 2-0 after Ramires tumbled under a challenge by goalkeeper Wojciech Szczesny, who as last man was fortunate to only receive a yellow card. The penalty was dispatched low into the corner for the midfielder's 195th goal for the club, leaving him seven behind Bobby Tambling's all-time record.
More chants of "Sign him up" came from the Chelsea fans, frustrated at the club hierarchy's apparent decision to let his contract run down this summer.
Ramires and the subdued Fernando Torres, recalled in place of Demba Ba, skied shots over as Chelsea toyed with Arsenal before the interval but the second half couldn't have been more different.
Chelsea surrendered a 2-0 lead to draw 2-2 with Southampton on Wednesday, virtually dashing the team's slim title hopes, and the same nearly happened five days on.
Walcott made it 11 goals in his last 15 appearances by running onto Santi Cazorla's perfectly weighted through ball and sidefooting a lofted finish past goalkeeper Petr Cech, sparking an all-out offensive from Arsenal.
Suddenly it was Wenger's team first to every ball as the home crowd became nervous but the equalizer never came, with Chelsea's defence — again missing the fit-again John Terry — holding form.
"It was very hard, the second 45 minutes," Mata said. "We were defending until the last minute."