Arsenal completed a Premier League double over city rivals Chelsea for the first time since 2003-04 after a narrow 1-0 win at Stamford Bridge.An uncharacteristic mistake from Jorginho allowed Arsenal to snatch an early lead through Emile Smith Rowe, and the Blues were never able to recover from that.Despite boasting a mammoth 68% possession in the game, Thomas Tuchel's side failed to create many chances. Christian Pulisic appeared to have scored the equaliser at the hour mark, but his effort was ruled out for offside.Arsenal, languishing near mid-table before the match, didn't threaten Chelsea for large swathes but maintained good defensive shape. The visitors were also aided by Bernd Leno's heroics between the sticks.🔴 @Arsenal completed their first #PL double over Chelsea since the 2003/04 season, with their first victory at Stamford Bridge since that famous 5-3 in 2011#CHEARS pic.twitter.com/2HkwIqunIJ— Premier League (@premierleague) May 12, 2021The defeat plunges the Champions League finalists down to fourth in the standings, two points off Leicester City, who pulled off a memorable 2-1 victory at Old Trafford last night. Arsenal, meanwhile, are up to eighth and suddenly in with a chance of qualifying for European football next season.On that note, let's have a look at the player ratings of both teams.ChelseaChelsea were left undone by Jorginho's error.Kepa Arrizabalaga - 7/10His name on the teamsheet initially raised eyebrows, but the out-of-favour Spaniard justified Thomas Tuchel's decision with a decent performance. The Chelsea custodian did well to save Jorginho's horrendous backpass but was beaten in the follow-up.Cesar Azpilicueta - 6/10It was not the best of games for the Chelsea captain, as he was given a torrid time by Arsenal's marauding forwards. That limited Azpilicueta's impact at the other end of the field.Thiago Silva - 7/10The veteran Brazilian centre-back held his ground well and looked decent in possession. However, Silva could have a tough time getting over the nutmeg by Smith Rowe.Kurt Zouma - 6/10It was an off day for the Frenchman, as he was nowhere near his best. Zouma did not make a single tackle or make a clearance either. He got a chance at the other end but blazed his effort wastefully wide.Reece James - 7/10He was energetic and made some darting runs forward. But James only looked dangerous after Giroud came on. The Englishman some good crosses, but Giroud failed to make the most of them.Billy Gilmour - 6/10Chelsea's rising star was underwhelming against Arsenal and was constantly overrun in midfield.Jorginho - 5/10A calamitous backpass to Kepa handed Arsenal an invaluable opening goal, but Jorginho found his feet as the match wore on.Jorginho’s error. Unbelievable. pic.twitter.com/x0pl0nqD0I— LDN (@LDNFootbalI) May 12, 2021Ben Chilwell - 6/10Chilwell made plenty of runs down his wing but couldn't really impact the game.Mason Mount - 7/10Mount was Chelsea's biggest threat again but often found himself boxed up in advanced areas and was denied a clear shot at goal with a superb block.Christian Pulisic - 6/10Pulisic produced a rather underwhelming outing. He rarely threatened Arsenal; he had the ball at the back of the net, but his effort was ruled out for offside.Kai Havertz - 6/10He should've taken his chance in the first half but lacked composure and ended up firing into the stands.Ratings of Chelsea substitutes against Arsenal:Oliver Giroud - 6/10Giroud missed a big chance in stoppage time, but credit must go to Leno for pulling off a good save.Callum Hudson-Odoi - 6/10Hudson-Odoi replaced Gilmour at half-time but barely proved to be an upgrade, as he cut an anonymous figure all night.Hakim Ziyech - 5/10Ziyech had very little time to light up the Bridge.