Mikel Merino scored the only goal of a disappointing contest at the Emirates as Arsenal pulled clear in second place and to within 12 points of runaway leaders Liverpool.
Chelsea badly missed the presence of the absent Cole Palmer due to illness as they meekly surrendered to a damaging defeat for their hopes of a top-four finish.
The Blues remain in fourth for now but have five sides from Manchester City in fifth to Aston Villa in ninth within four points of Enzo Maresca’s team.
Arsenal have struggled badly for goals since the loss of Kai Havertz to a season-ending injury has forced midfielder Merino into a makeshift centre-forward role.
The Spanish international proved the match winner from a corner as he looped a header from Martin Odegaard’s delivery inside the far post on 20 minutes.
Chelsea barely threatened but were nearly gifted a route back into the game when David Raya fumbled Marc Cucurella’s shot and the ball trickled wide.
At the other end, Chelsea’s Robert Sanchez made a brilliant stop to prevent Merino doubling Arsenal’s lead with the best effort of the second half.
But the game petered out with little goalmouth action as a limp performance will do little to quieten the critics of Maresca’s style of play among the Chelsea support.