Elijah Bryant made a jumper with 50 seconds left to give Elon a 72-71 lead. Then Blake Bozeman's basket gave Morgan State a one-point advantage with 15 seconds remaining.
Bryant led Elon (2-2) with 18 points and Eddy added 12.
Bozeman scored 16 points for Morgan State (0-5) and Kyle Thomas added 15. Cliff Cornish and Cedric Blossom added 11 apiece for the Bears.
Morgan State led 37-28 at halftime and Zech Smith's basket at the 7:41 mark gave the Bears a 19-point (66-47) advantage.
Eddy made a layup and hit four free throws to start a 12-0 run and Jack Anton capped it with a three-point play as Elon got within 68-66 with 2:58 left.