Leslie, one of five Wolfpack (10-2) players in double figures, picked up nine of his points at the free throw line and grabbed seven of State's 31 rebounds.
Richard Howell was 8-of-8 from the field en route to a total of 18 points and also had nine rebounds. T.J. Warren contributed 15 points.
The win extended the Wolfpack winning streak to six games.
Western (8-5) lost for the fourth time in six games. Nate Hutcheson led the Broncos with 16 points and Shayne Whittington scored 14.