The Blues were ahead after five minutes, however, when Eto'o curled one into the bottom corner from just inside the box.
It was 2-0 less than two minutes later when Schurrle found some space outside the box before drilling his shot into the corner of the net.
It got worse for Arsenal after 15 minutes when Kieran Gibbs was dismissed for handling the ball inside the box, despite replays showing that Alex Oxlade-Chamberlain had made the contact with his hand. Eden Hazard stepped up to send the home side 3-0 ahead from the penalty spot.
Chelsea came close to their fourth after 30 minutes when David Luiz struck an effort from distance, but a smart save from Szczesny prevented the home side from extending their lead.