An awful mistake by Jorginho led to Chelsea suffering a setback in their bid to seal a top-four finish.
They struggled to create chances at Stamford Bridge, where Emile Smith Rowe’s 16th-minute goal was enough to give Arsenal the points.
Jorginho’s horrendous back-pass required keeper Kepa Arrizabalaga to chase back and claw the ball away from the line to prevent an own goal.
Pierre-Emerick Aubameyang collected the loose ball and teed up Smith Rowe for a simple finish.
The goal came after Kai Havertz missed a great chance when he shot over when through with just Gunners keeper Bernd Leno to beat.
Chelsea had a second-half equaliser disallowed after an offside Christian Pulisic netted after Havertz had headed on Mason Mount’s left-wing corner.
And in injury time, Kurt Zouma’s looping header was pushed on to the bar by Leno and Giroud’s attempt to hook in the rebound also hit the upright.
The Blues remain fourth in the table and six points clear of fifth-placed West Ham, who have a game in hand.
Chelsea: Kepa, James, Azpilicueta (Ziyech 78), Silva, Zouma, Chilwell, Jorginho, Gilmour (Hudson-Odoi 45), Pulisic, Mount, Havertz (Giroud 65).
Subs not used: Mendy, Alonso, Werner, Emerson, Anjorin, Livramento.