Both sides had chances to win it in the second period, but the decisive strike came after 53 minutes when Laurent Koscielny could only convert a Juan Mata free kick into his own net.
Here, Sports Mole dissects the 90 minutes of action between the two sides.
On target 5
On target 5
Was the result fair?
On the balance of play, you would have to say just about. Chelsea certainly started the match the better and deserved to take an early lead. Arsenal, as expected, responded to level before the break, but there was something missing from their performance today. A point apiece would have perhaps best reflected the chances the two sides created, but Chelsea did look the more dangerous.
6/10. There were some positives from the home side, but they will certainly play better than today this season. The influential Santi Cazorla had a bit of an off-afternoon, while Gervinho, aside from his goal, was often left frustrated. Meanwhile, the manner of the two goals they conceded will leave Arsene Wenger raging.
7/10. The Blues were impressive this afternoon. They were not at their free-flowing best, but it was the solidity of their performance which impressed the most. Ramires and John Obi Mikel sat in front of the defence, allowing those ahead of them to link with Fernando Torres. Meanwhile, John Terry and David Luiz performed well in defence.
Sports Mole's man of the match
Ramires: The little Brazilian is perhaps best known for his powerful forward running, but he showed his discipline today with a wonderful anchorman display. He was just everywhere.
Biggest gaffe of the match
Arsenal's defending for Chelsea's opening goal was just woeful. Luiz was clearly unmarked in the penalty area and perhaps should have headed home, but Torres was on hand to finish behind him.
Martin Atkinson had a successful 90 minutes of work this afternoon. He rightly awarded a host of yellow cards in the opening period for a series of offences. Meanwhile, he waved play on when Torres fell over in the box before the interval.
Arsenal: The Gunners will look to return to winning ways when they face Olympiakos in the Champions League on Wednesday. In the league, they travel to West Ham United next weekend.
Chelsea: Chelsea will attempt to continue their winning run when they face FC Nordsjaelland in the Champions League on Tuesday. In the league, they play host to Norwich City next weekend.