The Blues hit the lead in the 20th minute when Fernando Torres cleverly got his foot to Juan Mata's free-kick to surprise the Gunners defence with the Spaniard's shot on the turn whizzing past Vito Mannone.
Chelsea were the better of the two sides by forcing their opposing defence into vulnerable positions but they managed to concede three minutes before half-time when Alex Oxlade-Chamberlain fed Gervinho with the Ivorian firing past Blues keeper Petr Cech.
The home crowd were calling for Arsenal to produce what they are so used to in the way of a win at home but Roberto Di Matteo's men managed to edge in front when Mata's free-kick failed to be cleared by Laurent Koscielny with the Frenchman turning it past Vito Mannone.
The Blues now find themselves four points on top of the Premier League table following their fifth victory from six outings as Arsenal drop to seventh.
Emirates Stadium, London - 60,101