Arsenal's Spanish defender Hector Bellerin will miss the rest of the season after being diagnosed with a knee cruciate ligament injury, the Premier League side announced on Tuesday.
Chelsea could have got a foothold in the game before half-time as David Luiz's header came back off the post.
The need for the riches as much as the prestige of a return to Champions League football leaves Arsenal little room for error when Chelsea visit the Emirates on Saturday.
Arsenal goalkeeper Petr Cech on Tuesday decided to call it a day from football at the end of the season.
Swiss midfielder Xhaka set Arsenal on their way with his fourth goal of the season.
"That is how I want the team to stay which is to be concentrated, nothing else."
Chelsea dominated possession at Stamford Bridge, but could not find a way past the inspired Jordan Pickford in the Everton goal to leave Sarri frustrated.
Performances have steadily improved and Emery's impact is already being felt.
Arsenal booked a place in the Europa League knockout stage and extended their unbeaten run to 15 matches despite a 0-0 draw with Sporting Lisbon, while Olivier Giroud's first goal of the season sent Chelsea through.
Arsenal are still waiting for a first statement win of the Unai Emery era, but the progress made by the Spaniard in his first three months in charge was clear to see as Liverpool left the Emirates content with a point from Saturday's thrilling 1-1 draw.
