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10-man Arsenal missed their chance to go back to the top of the Premier League after Diego Costa's goal dented their title hopes.
Per Mertesacker was sent off for a late challenge on Costa just moments before the Spain international popped up in the right place to convert a wicked cross by Branislav Ivanovic.
The result preserves the defending champions' unbeaten record under experienced Dutch manager Guus Hiddink, who took over as interim manager last month following Jose Mourinho's sacking.
Chelsea move up to 13th, while Arsenal are left in third place, level on points with Manchester City but three behind leaders Leicester City.
But who was the star man at the Emirates? See below for our player ratings from the London derby...
Show all 22 1 /22Arsenal 0 Chelsea 1 player ratings Arsenal 0 Chelsea 1 player ratings Petr Cech - 6 out of 10 Playing once more against his former side, the goalkeeper made several good saves to keep Arsenal in the game throughout, including a reflex stop to deny Willian but he couldn't do too much about Costa's goal after being let down by his teammates.
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Arsenal 0 Chelsea 1 player ratings Nacho Monreal - 4 out of 10 Put in a disappointing showing as he failed to stop Willian from running riot early on, and then did not stop Ivanovic from sending in the cross from which Costa scored from. However, he should get praise for denying the Chelsea right-back with a goal-line headed clearance.
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Arsenal 0 Chelsea 1 player ratings Per Mertesacker - 4 out of 10 Looked solid early on, but the towering defender let himself down in the 18th minute when he received a straight red card for his last-man challenge on Costa, which handed Chelsea the advantage they needed to go in front minutes later.
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Arsenal 0 Chelsea 1 player ratings Laurent Koscielny - 6 out of 10 Made one early misplaced pass that allowed Oscar to get a shot at goal, but was solid otherwise. Booked for a foul on Willian in the first half and was then fortunate not to give away a penalty for his body block on Fabregas in the second.
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Arsenal 0 Chelsea 1 player ratings Hector Bellerin - 6 out of 10 Struggled, at times, to deal with the pace of Azpilicueta, but was largely solid defensively although his impact going forward was limited due to Chelsea's good defensive work.
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Arsenal 0 Chelsea 1 player ratings Mathieu Flamini - 4 out of 10 Disappointed with his defending in the build-up to Costa's goal and wasted two good chances to get Arsenal back into the game when he first fell over while attempting to take a shot before driving another high before the break. A day to forget for the midfielder.
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Arsenal 0 Chelsea 1 player ratings Aaron Ramsey - 6 out of 10 Both he and Flamini couldn't control play in the middle of the park, and indeed it was Ramsey who failed to prevent Willian from sending in the ball that led to Chelsea scoring. However, he did have some good moments when building up Arsenal's attacks, but saw his teammates make little use of his hard work.
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Arsenal 0 Chelsea 1 player ratings Joel Campbell - 5 out of 10 Could have done more defensively in build-up to Chelsea's opener and disappointed when going forward. Was replaced by Sanchez in the second half.
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Arsenal 0 Chelsea 1 player ratings Mesut Özil - 5 out of 10 Had a few good moments when going on the attack, but ultimately saw his impact limited by some good marking from the likes of Matic and Mikel.
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Arsenal 0 Chelsea 1 player ratings Theo Walcott - 5 out of 10 Captained the side despite Mertesacker starting the game, but couldn't make the difference up front; being flagged offside twice in the first half and then blocking Sanchez's shot that seemed to be heading towards goal.
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Arsenal 0 Chelsea 1 player ratings Olivier Giroud - 5 out of 10 The striker had some positive moments early on although he did blast a speculative shot high, but was sacrificed for Gabriel after Mertesacker had been sent off. Had never scored a career goal against Chelsea, and that remains the case after seeing his game cut short.
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Arsenal 0 Chelsea 1 player ratings Thibaut Courtois - 6 out of 10 Was rarely tested in the first half, but looked comfortable when called into action.
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Arsenal 0 Chelsea 1 player ratings Branislav Ivanovic - 7 out of 10 Just days after signing a new one-year deal and Hiddink stresssing the right-back is back to his best, Chelsea's vice captain looked like a rejuvenated player. He helped get involved in the visitors' attacks regularly and was rewarded when he delivered the cross from which Costa scored from. Saw a header just before the break cleared off the line by Monreal.
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Arsenal 0 Chelsea 1 player ratings John Terry - 6 out of 10 Had one nervy moment when Giroud ran past him to create an Arsenal attack, but he made up for it by blocking the Frenchman's later shot. Impressive otherwise.
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Arsenal 0 Chelsea 1 player ratings Kurt Zouma - 7 out of 10 Was as solid as ever at the heart of Chelsea's defence, and demonstrated once again why he is a mainstay in this team.
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Arsenal 0 Chelsea 1 player ratings César Azpilicueta - 7 out of 10 On his 150th start for Chelsea and his 100th Premier League start, the left-back enjoyed a good showing as his forrays forwards helped Chelsea overrun Arsenal while he used his pace to get back and defend.
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Arsenal 0 Chelsea 1 player ratings John Obi Mikel - 6 out of 10 Alongside Matic, Mikel had no real problems in dominating play in the midfield positions and protected his back line superbly. Booked for challenge on Sanchez.
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Arsenal 0 Chelsea 1 player ratings Nemanja Matić - 7 out of 10 Making his 100th Chelsea appearance, the Serb showed purpose in attack for the Blues as he got into good positions several times - for example when he was involved in the build-up to Costa's goal - while impressing when defending. His run back to his own box to stop Bellerin from launching an optimistic counter-attack was one such moment. Booked for foul on Sanchez.
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Arsenal 0 Chelsea 1 player ratings Willian - 7 out of 10 Won the battle with Monreal time and time again and was involved in many of Chelsea's best chances including one of his own that Cech saved. The Brazilian was also instrumental as it was his ball to Costa that led to Mertesacker's red card. Did not neglect his defensive work either.
Arsenal 0 Chelsea 1 player ratings Cesc Fàbregas - 7 out of 10 Started the game further forward against his former side and helped dominate play in the middle of the park - pulling the strings throughout the game and being rewarded when he helped carve out Costa's goal. Unlucky not to have been given a penalty for Koscielny's foul on him.
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Arsenal 0 Chelsea 1 player ratings Oscar - 6 out f 10 Began the game in the unfamiliar position on the left flank with Eden Hazard not risked and, despite a yellow for a wild challenge on Campbell, the Brazilian impressed with good attacking and defensive play particularly in the first half. Was replaced by Hazard with 15 minutes to go.
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Arsenal 0 Chelsea 1 player ratings Diego Costa - 8 out of 10 The striker was the centre of headlines the last time these two sides met in the season and he proved so again today. It was his run forwards that forced Mertesacker into his last-ditch tackle, for which he was sent off for, before Costa helped create and then finish off Chelsea's opening goal. Costa was impressive considering he hardly trained this week following his bruised tibia against Everton but he paid for it when he came off with an injury in the second period.
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The Gunners next face Burnley in the FA Cup while Hiddink's men travel to MK Dons.
A tough match against Southampton then awaits Arsenal in the Premier League as Watford entertain the Blues.
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