Cochran moved into seventh on the school's all-time scoring list with 1,793 points.
C.J. Neumann added 10 points, on 4-of-5 shooting, and seven rebounds for Wofford (21-6, 12-2 Southern Conference), which hadn't won at Western Carolina (13-14, 8-7) since Feb. 19, 2001.
The Terriers took a 37-23 lead early in the second half when Cochran hit a 3-pointer, but Western Carolina used a 12-2 run to pull within three with 16 minutes left.
Wofford, which shot 50 percent overall and hit a season-high 13 3-point shots, responded by scoring nine of the next 11 before pushing its lead to as many as 22 points.