John Brown and Devante Wallace both added 13 points for High Point (16-5, 7-2 Big South), which took a 61-51 lead on Cugini's 3-pointer with 51 seconds left.
High Point broke a 34-all tie early in the second half with a 6-0 run to take the lead for good. The Blue Hose (7-15, 3-6) stayed within eight points and got as close as 54-51 with 2:59 left until High Point's 7-0 run.
Ed Drew led Presbyterian with 12 points. DeSean Murray scored 11 and Jordan Downing added 10. Presbyterian's leading 3-pointer shooter, Downing (40.5 percent), was 1 of 8 from the arc and the Blue Hose were 3 of 16 as a team.
The Panthers were 10 of 21 from 3-point range and 23 of 44 from the field.