But Nketiah added his second early in the second half and a Chelsea team featuring Romelu Lukaku leading the attack this time had no response. Bukayo Saka made sure of the vital three points when converting a stoppage-time penalty.
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The victory snaps a three-game losing streak for Arsenal and lifts back level on points with fourth-placed Tottenham and three points ahead of Manchester United, who have played a game more, in sixth.
Despite defeat, Chelsea maintain a five-point cushion in third and have a game in hand on both Arsenal and Tottenham.