Casillas got out of position rushing out to meet a cross, and Godin outjumped Sami Khedira to loop a header into the goal.
Three minutes earlier, Gareth Bale wasted Real's best chance, scooping a left-foot shot wide after exploiting Atletico midfielder Tiago's misplaced pass.
Atletico's gamble on forward Diego Costa's injured right hamstring backfired as he lasted just nine minutes before being replaced by Adrian Lopez.
In the 26th, Atletico's Raul Garcia escaped with a yellow card for bringing down Angel Di Maria to stop a fast break.
Cristiano Ronaldo fired the resulting free kick direct at goalkeeper Thibault Courtois.