The 49ers (3-2) took the lead for good shortly after the 15-minute mark at 47-46 and pushed the margin to 10 after the midpoint of the half.
The Panthers (2-3) had a late 6-0 run to close the deficit to three on Brandonn Kamga's basket with 12 seconds left. Luka Vasic missed both free throws for Charlotte with nine seconds left, but Andre Fox missed a 3-point attempt that would have tied it in the final seconds.
Kamga finished with a career-high 26 points and Fox added 10 for High Point.
Charlotte led by as many as 11 in the first half and went into the break with a 38-33 lead. High Point had an 11-3 run early in the second for its only lead at 46-43.
No. 20 Arizona State seeks second straight win vs. SEC foe at Vanderbilt
No. 20 Arizona State engineered an 18-point comeback to beat Georgia on Saturday, and the deciding basket came on a play that illustrates the difference between this year's group and last year's perimeter-oriented NCAA Tournament team.
No. 10 Florida State returns from break to host Southeast Missouri
After eight days off for final exams, 10th-ranked Florida State gets back to work on the court Monday night against Southeast Missouri State.
Bryce Drew, Vanderbilt and how to manage a crisis
Vanderbilt was supposed to take a leap this season. Then, the Commodores lost their best player. It's up to Bryce Drew to figure out what happens next.