Theo Walcott pulled a goal back for the Gunners, but they couldn't find an equaliser as Chelsea held on to claim all three points.
Here, Sports Mole takes an in-depth look at how Chelsea got the win in a thoroughly entertaining match.
On target 8
On target 8
Was the result fair?
Overall, a draw was probably the fairest result. It was the cliched 'game of two halves', with Chelsea dominating the first period and Arsenal the second. The Blues made more of their time in charge of the match, however, and their first-half performance is what got them the win, so it wasn't exactly an unfair result either.
In the first half, they were very good. They were given space to play and made the most of it, with their midfield being particularly dominant. Their second-half performance wasn't as bad as it was against Southampton in their last outing, but they were still outplayed and were on the ropes at the end of the match.
The direct opposite of Chelsea's. In the first half they were poor, giving the likes of Mata, Ramires and Eden Hazard too much space, for which they were punished. However, in the second half they looked like a different team, closing the opposition down and creating a lot more chances. They didn't quite do enough to find an equaliser, but they were certainly knocking on the Chelsea door and had by far the better of the second period.
Sports Mole's man of the match
Ramires: This is quite a tough call considering how the game went, but Ramires's first-half performance was very strong. His bursting runs from midfield caused the Arsenal defence lots of problems, and one such run directly led to the penalty which provided Chelsea's second. Juan Mata also deserves a mention, as he pulled the strings in the first half.
This has got to be Demba Ba's miss. It didn't end up having an effect on the result, but the former Newcastle man really should've scored having rounded Wojciech Szczesny. Thomas Vermaelen got back brilliantly to clear the ball off the line, but Ba should have put the game to bed.
It was a strong performance from Martin Atkinson. He had two big decisions to make - the penalty and the resulting punishment - and I think he made the correct decision on both occasions. Ramires may have gone down a bit easily for the spot kick, and may have tripped over Szczesny rather than being tripped by the keeper, but from the referee's view he had no choice. He could, and perhaps by the letter of the law should, have sent Szczesny off, but not doing so helped the game and was a good decision.
Chelsea: Chelsea return to cup action next, taking on Swansea in the League Cup semi-final on Wednesday before an FA Cup fourth-round match against Brentford next Saturday.
Arsenal: The Gunners have a midweek Premier League tie against West Ham United before taking on Brighton & Hove Albion in the FA Cup.