Whittington sank three 3-pointers and stole the ball four times in the win, which was the 42nd in a row at home against non-conference opponents for the Hoyas (9-1).
Jabril Trawick added 14 points and Otto Porter scored a dozen to go along with eight of Georgetown's 32 rebounds.
Tom Tankelewicz led Western Carolina (4-7) with a career-best 24 points and Trey Sumler came off the bench to score 11 points and notch three assists Tankelewicz was 6-of-10 from 3-point range.
Georgetown held a 42-30 lead at halftime and fended off the Catamounts in the second half. Western Carolina lost for the third time in its last four games.