Boggs scored nine points in a 14-4 run for the Catamounts (9-15, 6-6) at the start of the second half that gave them a 48-38 lead with 13:21 remaining.
The Catamounts ended a four-game losing streak, which included a 72-66 home loss to Georgia Southern on Jan. 26.
Western Carolina shot 52.7 percent (29 of 55) in Saturday's game to 36 percent (18 of 50) for the Eagles (10-15, 4-8), whose 54.9 percent shooting in the first meeting was the best by a Catamounts opponent this season.
Washington State's trio of Josh Hawkinson, Conor Clifford and Ike Iroegbu have withdrawn from the NBA draft and will play their senior season with the Cougars.
Gonzaga center Przemek Karnowski, who missed most of last season with a back injury, says he is returning for another year.
Wisconsin forward Nigel Hayes has withdrawn from the NBA draft and will return to the Badgers for his senior season.