Keith Hornsby added 12 points to help UNC Asheville (11-10, 5-2) win its third straight game.
Trailing 28-26 at halftime, UNC Asheville took the lead 38-36 on Atkinson's layup with 16:03 remaining. The Bulldogs then used an 18-10 run to push the lead to 56-46 with 8:18 left to play.
High Point (9-10, 4-3) would get within five points, 59-54 on Corey Law's dunk with 3:45 to go, but UNC Asheville closed out the game on a 10-4 run. The Panthers went scoreless in the final 2:17.
After shooting just 33.3 percent (10 of 30) in the first half, UNC Asheville improved to 61.9 percent (13 or 21) in the second.
Law led the Panthers with 13 points and seven rebounds.
Maryland point guard Melo Trimble, considered a lock to leave the program before struggling in the second half last season, has withdrawn from the NBA draft and will return for his junior season.
Louisville's Chinanu Onuaku, who recently underwent a medical procedure to correct a heart rhythm issue detected during the combine, will keep his name in the NBA draft pool.
Andrew White III will return to the Nebraska men's basketball team next season after removing his name from the NBA draft.