Allison finished with 10 points and 15 rebounds as the Black Bears (9-10, 3-5 America East Conference) won the battle of the boards 40-34.
The Black Bears shot better than Maine from the field, 42.6 percent (23 of 54) to 40.4 percent (23 of 57) but allowed 19 points off of 14 turnovers.
Gerald McLemore added 15 points for Maine, which scored 30 points in the paint.
The Black Bears led 31-24 and stretched their lead to as many as 20, 47-27 on Allison's layup with 15:09 to go.
Towson picked up its first victory of the season, beating UNC Wilmington 66-61 on Saturday.
- Sports & Recreation/Basketball
- Sports & Recreation
- Mike Allison
- America East Conference