Joe Knight's three-point attempt at the buzzer bounced off the back rim and the Chanticleers picked up their second huge road win in as many tries.
Danny Gathings led all scorers with 29 points, while Dustin Van Weerdhuizen added a season-best 22 points for the Panthers.
Coastal got 17 points from Albany transfer E.J. Gallup (which ties his career-high). Also in double-figures were Tony Darden (15 points), Mihai Raducanu (a career-best 12 points), and Torrey Butler (10 points).
The game, which CCU lead 39-35 at intermission, featured 18 lead changes, but none following Derrick Robinson's layup with 4:17 to got that put the Chants up 68-67 and sparked a 7-0 run.
Two Van Weerdhuizen free throws and a foul shot by Gathings brought the Panthers within 74-70. Following a Darden tip-in with 51 seconds left, Van Weerdhuizen made back-to-back layups to pull HPU within 76-74 with 26 seconds to play.
Butler was fouled and missed a free throw with 17 seconds to go, but Clint Nagel came up with a huge offensive rebound. Nagel then missed his foul shot, but Darden was called for a foul on the rebound. Brent Halsch then hit one of two foul shots on the other end with 16 seconds left to pull HPU within 76-75.
CCU freshman Colin Stevens was fouled with six seconds to play and made one of two shots. HPU head coach Jerry Steele called a time out with 2.8 seconds left to set up the possible game-winning shot, and the ball went in to Knight, who had a decent look at the basket, but the shot bounced off the back rim and the Chants escaped.
Coastal has now won five of its last six and wraps up the three-game Big South Conference road trip at Elon, Mon., Nov. 13 at 7 p.m.