Cheslea 3-2 Arsenal: Marcos Alonso scores late winner (Match Highlights)
Alonso slot the ball through Cech's legs from close range after Eden Hazard picked him up with a pass in the box.
Arsenal's new coach Unai Emery has now lost his first two games this season leaving Arsenal with zero points.
The first 45 minutes saw four goals scored by both teams.
Pedro tapped in from close range after some poor defending by Arsenal with just nine minutes on the clock.
In the 20th minute, Alvaro Morata took the initiative as he beat a high line offside trap by a woeful Arsenal defense to make it 2-0.
Pierre-Emerick Aubameyang and Henrikh Mkhitaryan missed clear-cut chances for the gunners after each Chelsea's goal.
The visitors got themselves back in the game with Mkhitaryan scoring from just outside the box in the 37th minute, and Alex Iwobi scored with a good finish inside the box to draw level three minutes before the end of the half.
Arsenal could not hold on again to let Marcos Alonso score a late winner after some fine play by Eden Hazard to find him in space in the box, maintaining Maurizio Sarri's 100 per cent start to life in the Premier League.