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.
Toddler uninjured after being knocked over by Obama family dog
Ron Burgundy interviews Peyton Manning on SportsCenter