Abreu was 7 of 13 from the field, knocking down four 3s in the process. Benson was 9 of 10 and made his only 3-point attempt.
New Hampshire (8-15, 3-9 American East Conference) entered halftime trailing 27-25 but opened the second half on an 18-6 run to take a 43-33 lead with 13:29 left to play.
Albany (15-11, 7-5) rallied to tie the game 61-all with 1:53 remaining but Benson made a layup and Ferg Myrick converted a three-point play to seal the victory.
Myrick had 19 for the Wildcats.
The Wildcats had 15 team assists, compared to just six for Albany, and won the rebounding battle 33-28.
Gerardo Suero led Albany with 20 points but struggled from the field, hitting only seven of his 20 attempts.