The Hilltoppers (4-2) had trouble pulling away from the NAIA Bearcats (2-6).
Leading 23-22, Crook made a layup at the 6:36 mark, sparking an 11-3 run to close out the half.
Western Kentucky then opened the second half with a 16-2 spurt. Brescia didn't hit its first two-point basket of the stanza until Myron Christian's layup with 9:11 remaining.
The Hilltoppers shot 44.6 percent from the field (25 of 56), but a woeful 4.8 percent from long range (1 of 21) and made only 57.5 percent of their free throws (23 of 40).
Christian scored 15 to lead Brescia, which shot just 23.4 percent from the field (11 of 47).