After securing a slender 1-0 advantage in the first leg last week, the Citizens played out a goalless draw at the Wanda Metropolitano on Wednesday night, which was marred by unsavoury scenes towards the end of the game.
Browsing: Stefan Savic
Morocco forward Ziyech grabbed his first goal since October to put the hosts ahead in the first half at Stamford Bridge.
United States midfielder Tyler Adams snatched victory in the 88th minute with a strike from outside the box, which took a heavy deflection off Atletico defender Stefan Savic to flummox goalkeeper Jan Oblak.
Mexico midfielder Hector Herrera leveled in the 90th minute with a thumping header from a corner in the Champions League first game clash
Espanyol are 15th in the standings and had only won one of their previous seven games
While Atletico will drop into the Europa League, Chelsea face the prospect of playing either Barcelona or Paris Saint-Germain at the last-16 stage of this competition after Christmas