Tremayne Dameron added touchdown runs of 5 and 3 yards as the Tigers (2-3, 1-1 Colonial Athletic Association) scored on each of their first three possessions to take a 20-0 lead with 7:21 left in the first quarter.
Athens, who was 11 of 21 for 188 yards, also rushed for 74 yards. Moore finished with 91 yards on four catches for Towson.
Rhode Island (1-4, 0-2) used two big plays to cut the deficit to 20-14 at the half. Ayo Isijola scored on a 48-yard run with 6:03 left in the second quarter, and Shawn Leonard caught a 35-yard pass from D.J. Stefovich with 3:06 remaining before halftime.
Isijola finished with 100 yards rushing and Stefovich was 11 of 20 for 163 yards and three touchdowns.