Down 14 points with 9:37 to go, Kostic drained his second trey to pull Appalachian State within 67-66 with 2:06 to play. His third 3 gave the Mountaineers their first lead of the second half, 72-71, with :51 left.
The Red Wolves couldn't answer when Sean Gardner's shot missed with two seconds left.
Frank Eaves scored 22 points, and Kostic finished with 11 for Appalachian State (4-6, 1-0 Sun Belt Conference).
Livingston had 21 points and 13 boards, and P.J. Hardwick had 10 points and 15 assists for Arkansas State (6-5, 1-1).