Eden Hazard scored a magnificent goal for Chelsea against Arsenal
Alex Iwobi had an early chance for Arsenal after he latched on to a stray pass from Thibaut Courtois, and his low drive crept a fraction wide.
But it was Chelsea who took the lead when Pedro crossed for Diego Costa.
The striker's header thumped the bar, but Marcos Alonso was able to beat Hector Bellerin to the rebound and head home.
Chelsea began to take control of the game and Costa flashed a shot from inside the area into the side netting.
Marcos Alonso got Chelsea's first of the afternoon
But Arsenal almost levelled when Francis Coquelin's delivery was met by Gabriel, but Courtois produced a fine one-handed save to keep the Blues ahead.
Mesut Ozil then had a great chance to level proceedings just before the break, but he took an extra touch to cut onto his left foot and his low drive was easily held by Courtois.
And after the break Chelsea went further ahead after a wonderful goal from Eden Hazard.
The Belgium international picked up the ball up in his own half, held off Coquelin before getting round Laurent Koscielny and firing past Petr Cech.
Should Chelsea's goal have stood after this challenge on Hector Bellerin?
Sat, February 4, 2017
Should have Chelsea's opening goal against Arsenal stood after this challenge on Hector Bellerin
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Should Chelsea's goal have stood after Alonso's challenge on Bellerin?
Despite being two behind, Arsenal kept fighting and they could have had an equaliser when Nacho Monreal crossed, but there was no one waiting in the box.
Danny Welbeck next tried his luck, but Courtois kept out his downward header.
And Chelsea killed the game off when former Arsenal man Cesc Fabregas scored after an error from Cech.
Olivier Giroud grabbed a late consolation for Arsenal but the Blues are now 12 points clear at the top of the table and remain on coure to win the Premier League title.