Iati (20 points) was 6 of 14 from the field with all six makes coming from deep. Peter Hooley chipped in 11 points for Albany (8-2). Iati, Hooley, and Black accounted for 13 Albany free throws.
Tied at 11, Blake Metcalf's jumper sparked a 15-0 run by Albany. Iati's 3-pointer capped the run.
Colgate (3-7) outshot Albany 42 percent (25 of 60) to 41 percent (22 of 54) and outrebounded the Great Danes 39-34, but made just 9 of 14 free throw attempts.
Albany, which made 15 of 20 free throws, hit six over the final 51 seconds while holding Colgate to just two field goals.
Murphy Burnatowski was Colgate's lone player in double-figures with 13 points.
Maryland point guard Melo Trimble, considered a lock to leave the program before struggling in the second half last season, has withdrawn from the NBA draft and will return for his junior season.
Louisville's Chinanu Onuaku, who recently underwent a medical procedure to correct a heart rhythm issue detected during the combine, will keep his name in the NBA draft pool.
Andrew White III will return to the Nebraska men's basketball team next season after removing his name from the NBA draft.