The Tribe (5-4) won for the fourth time in five games.
Julian Boatner's basket with 1:25 left gave the Tribe the lead for good at 59-57, and two free throws had them up by four with 35 seconds left.
Wofford's Indiana Faithfull then drove to the basket, scored and was fouled. His free throw cut the lead to 61-60. The Terriers (3-5) pressed and forced a turnover but Jaylen Allen's floater in the lane missed. Kyle Gaillard wrapped up the win with a pair of free throws with a second left.
William & Mary shot 56.1 percent, led by the strong inside game of Rusthoven, who made 5 of 7 shots.
Kapita was the top-rated recruit from West Virginia in the class of 2015 and recently played at DME Academy in Florida.
With the Suns drafting Tyler Ulis, they now have five guards on their roster who attended Kentucky.
NBA fans will be looking forward to their newest players making plays like this next season.