Video: Arsenal 0-1 Chelsea [Premier League] Highlights 2015/16
The Gunners were reduced to 10 men after just 18 minutes, Mertesacker bringing down Costa after the striker had been sent clean through by a precise ball from Willian.
The Spain international then poured further misery on Arsene Wenger’s side, guiding home Branislav Ivanovic’s cross at the near post for the only goal of the game.
Even the second-half introduction of Alexis Sanchez – featuring for the first time since suffering a hamstring injury in November – could not spark Arsenal, who lost at home in the league for the first time since the opening weekend of the season.
Victory means Chelsea remain unbeaten since Guus Hiddink replaced Jose Mourinho and they have not lost in their last nine league meetings with Arsenal, who are third, three points behind leaders Leicester City.