The Tigers (6-1, 4-0), who had lost 26 of their previous 28 conference games entering this season, are off to their best start since moving up from Division II in 1987.
The victory over the Tribe (4-4, 2-3) was their first in eight tries.
West, who carried 23 times for 141 yards, scored twice on 2-yard runs and once from 6 yards to give Towson a 28-10 second-quarter lead.
Jonathan Grimes capped a 16-play, 72-yard drive for the Tribe with a 1-yard run that made it 28-17 with 21 seconds left until halftime. Grimes finished with 133 yards on 30 carries.