Simuel Frazier added 12 points and six assists to help Howard (3-8) overcome a first-half deficit.
Trailing at halftime 32-25, Thompson's steal and fast-break layup to begin the second half sparked a 15-1 run, helping Howard take a 40-33 lead with 12:06 left to play. Thompson capped the run with a three-point play.
With 44 seconds left to play and down by three, Liberty's (1-9) John Caleb Sanders was fouled on a 3-point shot and converted just two of three free-throws to cut the deficit to one, 54-53.
Howard answered making 6 of 8 free throws down the stretch to seal the victory.
Liberty shot just 24.1 percent (7 for 29) in the second half.
Davon Marshall led the Flames with 13 points.