Tanner Leissner's 3-pointer gave New Hampshire a 71-70 lead in OT, but Singletary hit back-to-back 3-pointers and Albany led 76-73.
Singletary made 5 of 9 3-pointers, Ray Sanders scored 17 points, and Cremo added 13 for the defending America East Conference-champion Great Danes (14-4, 3-0).
Trailing by two at halftime, New Hampshire rallied to lead 68-66 after Daniel Dion's two free throws. Sanders made a layup to tie it a 68 at the end of regulation.
Leissner scored 21 points, Smith added 14, Dion 13 and Joe Bramanti 11 for New Hampshire (8-7, 1-1).