You don't need a comma after Heart.
The rest is correct.
Have you ever read the story, "The Tell-Tale Heart," by Edgar Allan Poe? Dave asked.
Have I written this correctly?
4 answers
This site may help you.
http://leo.stcloudstate.edu/research/puncquotes.html
http://leo.stcloudstate.edu/research/puncquotes.html
If you keep the comma after "story," then you need the comma after "Heart," too.
"Have you ever read the story, 'The Tell-Tale Heart' by Edgar Allan Poe?" Dave asked.