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.
There's nothing to suggest the Jayhawks won't end up atop the Big 12 for a 13th season in a row. But what about a return to the Final Four?
Colorado State graduate transfer John Gillon has chosen Syracuse, giving the Orange a potential starter at point guard entering the 2016-17 season.
DeSean Murray, who averaged 20.2 points as a sophomore at Presbyterian, will transfer to Auburn to play for coach Bruce Pearl.