This is one of Poe’s most suspenseful short stories. Like much of this story, the suspense in the climax is psychological. The story basically centers on the narrator, who is struggling with insanity. He kills the old man, his roommate, because of his evil eye.
The climax of the story is not when the narrator kills the old man, cuts him up, and buries him under the floorboards. Instead, the climax is when the narrator is driven mad by the old man’s still-beating heart, which he can hear in his mind.
The climax of the story is suspenseful because the police come and the start looking around, and the narrator makes small talk and tries to be casual and clever. He even has the policemen sit in the same room where the body is buried! Alas, he is driven so mad by the imaginary beating heart that he confesses.