How did Cobb manage to go to sleep and dream to save Saito after Mal's death?

It is true that one needs to fall asleep in order to dream, and for such deep, consistent sleep the extractors use sedatives. But in the scene which you are referring, where Mal dies by Ariadne, Cobb never goes to sleep. He is able to deduce that Saito must be dead by now and floating in limbo. Thus he takes the leap from the building, so that he dies in that dream and he too enters limbo.