Justin Browning and Rhett Harrelson scored 15 apiece while Torrion Brummitt scored 14 and Mike Brown 10. The Catamounts (6-8, 1-1) were outshot 51.2 percent (21-41) to 47.4 percent (27-57) and outrebounded 32-23.
The Citadel led 10-5 after a layup by Quinton Marshall, but Western Carolina stayed close. The lead changed hands eight times with four ties before Sinclair hit a jumper and the Catamounts led 37-36 at halftime.
Western Carolina opened the second half with a 14-2 run, but the Bulldogs rallied, pulling within four, 74-70, after a free throw by Marshall with 10 seconds left. The Catamounts finished with four unanswered points.