The meeting, held in Moscow at the VEB Arena, ended 2-0 in favor of the guests.
Espanyol's victory was brought by goals by Lei and Victor Campusano, who scored in the 64th and 95th minutes.
In the third round, CSKA will host the Hungarian Ferencvarosh on their field, and Espanyol will play against the Bulgarian Ludogortsev away.
Earlier, the starting lineup of Krasnodar for the match of LE with Getafe became known.