First responders to Chris Cornell's Detroit hotel room were delayed in their efforts to save him because they had to get him down from the door he used to hang himself ... according to the 911 call.

On the just-released call you can hear an MGM Grand Detroit employee tell the dispatcher staffers had been unable to give Chris CPR due to the exercise band around his neck. 

As we reported ... the Soundgarden frontman used common exercise equipment attached to a carabiner to take his own life.

The toxicology report later revealed Chris had several prescription drugs in his system. He was 52.