The players accounted for 35 of the 39 Hilltoppers' bench points. Harrison-Docks and Snipes combined to shoot 50 percent (10 of 20) from the field.
Ben Lawson finished with 12 rebounds and three blocks for Western Kentucky (6-4).
Ladarius Tabb's layup with 17:21 to play gave the Bulldogs a 47-39 lead. But Western Kentucky used a 12-1 run over the next four minutes to take a 50-48 lead on Chris McNeal's 3-pointer and never trailed again.
Western Kentucky has now won back-to-back games for the first time this season. The Hilltoppers have won six-straight at home and are 23-4 at E.A. Diddle Arena in their last 27 games.
Tabb finished with 27 points and nine rebounds for Alabama A&M (4-3).