Finn, a 6-foot-2 sophomore guard averaging just 7.2 points per game this season, made 7 of 9 3-pointers and also had four steals and three assists for the Red Wolves (7-8, 2-0 Sun Belt).
Martavius Adams added 12 points and eight rebounds and Donald Boone had 10 points and eight rebounds for the Red Wolves, who outscored the Hilltoppers (5-8, 0-1) 41-34 in the second half to pull away.
Sergio Kerusch connected on 11 of 16 shots, scoring 25 points to lead Western Kentucky. He also had six rebounds. Juan Pattillo added 16 points and nine rebounds while Steffphon Pettigrew had 14 points and seven rebounds for the Hilltoppers.
Western Kentucky had won the previous five meetings against Arkansas State, which included three wins last season. The Hilltoppers eliminated the Red Wolves from the Sun Belt tournament last spring.