Cochran, who scored 10 of his points in the first half, also grabbed seven rebounds while Loesing dished eight assists and shot 7 of 11 from the floor.
Charleston led 3-2 in the first half, but it was the last time the Cougars would see the lead, as Cochran made a jumper to spark a 21-10 run and give the Terriers (14-8, 7-3 Southern Conference) a 24-12 lead.
Wofford took a 28-19 lead into halftime and matched the Cougars (12-9, 4-6) basket for basket in the second half.
Trent Wiedeman led Charleston with 18 points but the Cougars shot 37.9 percent (22 of 58) from the field and received no points from the bench. Charleston's bench went a combined 0 for 8 from the field.