A goal from Emile Smithe-Rowe in the 16th minute which came about because of a Jorginho mistake was all it took to give Arsenal the victory and achieve the double over their London rivals for the first time in 17 years.
That was the only goal in a tepid game that saw Chelsea with almost 70% of ball possession but they lacked a distinct cutting edge.
Chelsea remain fourth on the table and the chase for the Champions League slots will likely not be settled until the last day of the league.
Chelsea have 64 points while the chasing pack led by West Ham have 58 points; Liverpool with 57 points have two games in hand while Tottenham and Everton are still in the mix.
Kai Havertz should have given Chelsea the lead in the 10th minute when he robbed Pablo Mari of the ball and went into the box but he then blasted over with just Bernd Leno to beat.
Six minutes later, Jorginho played a blind back pass that was saved on the line by Kepa Arrizabalaga, who was one of the five changes Thomas Tuchel made for the encounter.
Mason Mount had a shot in the box in the 22nd minute but from the penalty spot, Rob Holding made a fantastic block on what would have surely been the equaliser. Leno then made a good save from Mount in the 26th as Chelsea pressed for the equaliser and Arsenal defended deep. Three minutes later, Christian Pulisic headed over a half chance.
The second half was more of the same as Tuchel sent on Callum Hudson-Odoi. Two minutes after the resumption, Havertz went down in the box and there were penalty shouts but referee Andre Mariner waved play on. Pulisic thought he had the equaliser with a header on 61 minutes but he was yards offside.
In the dying seconds of the match Kurt Zouma’s header was saved but off the rebound, substitute Olivier Giroud smacked the ball off the same crossbar as Arsenal held on to take all three points to give themselves a glimmer of a chance to sneak into the Europa League.
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