
Meanwhile Swansea gave new coach Francesco Guidolin victory in his first game in charge with a 2-1 win away to Everton as the Welsh club moved four points clear of the relegation zone.
At the Emirates, Arsenal were reduced to 10 men in the 18th minute when Per Mertesacker was sent off for a challenge on Chelsea striker Diego Costa, with referee Mark Clattenburg ruling the Gunners defender was the last man.
Four minutes later, Costa gave Chelsea the lead when he got on the end of a Branislav Ivanovic cross at the near post.
Arsenal's defeat left them in third spot, three points behind shock leaders Leicester City, while Chelsea moved up into 13th place.
For all their contrasting fortunes this season, Chelsea are now unbeaten in nine league games against Arsenal and Blues skipper John Terry told Sky Sports: "It is a good three points and gets us up the league. We've drawn too may of late so we needed to pick up three points
"Mentally we were sound and on top. As soon as they had the man sent off they sat back so we pressed up higher and won the ball back. We are delighted with the win."
As for where Chelsea might finish this season, central defender Terry added: "Anything is doable. Everybody is beating everybody else. It is a tough league and if we put a run together we have a good chance (of fourth). We will fight until there are no points to play for."
Arsenal goalkeeper Petr Cech, who joined the Gunners from Chelsea in pre-season, said the home side had been unlucky.
"For 60 minutes, we were the better team and showed great character, we just needed a bit of luck to find the net." ?AFP