Western (2-0) fell behind by as much as 22-13 with 10:47 left in the first half, and Wesleyan (2-1) was behind only 46-45 at halftime after Lee and Brazelton keyed a late run.
Lee scored eight of the Hilltoppers' first 12 points in the second half as Western pulled out to a 62-52 lead with 10:54 left to play.
Western ended the game on a 21-9 run over the final eight minutes for the win.
Orlando Mendez-Valdez scored 20 points for Western, shooting a perfect 6-of-6 from the field and 3-of-3 from 3-point range.
Western Kentucky's defense tightened in the second half thanks to constant full-court pressure, holding Kentucky Wesleyan to 35 percent shooting after giving up a 63 percent clip in the first half.