The breakthrough came in the 22nd minute when Militão unleashed a powerful shot from well outside the box, leaving the Espanyol goalkeeper with no chance as the ball found the top corner.
Just two minutes into the second half, Mbappé doubled the lead. The French international, who has been in sensational form, connected with a pass from Vinícius Júnior and fired a precise strike from the edge of the area into the bottom corner. The goal marked his seventh goal in six games for Madrid this season.
The victory, a comfortable one for Xabi Alonso's side, moves Real Madrid five points clear at the top of the La Liga table and hands Espanyol their first loss of the season.