They also turned the ball over with 10 seconds left, leading to Albany being able to all-but run out the clock.
Stepehen Weigh led the Utes with a career high 22 points. Luke Nevill added 17 points.
Nevill put the Utes up 58-57 with jumper as the shot clock expired, but Albany answered a minute later with a fast break lay-in that put them up for good.
Utah falls to 5-8, their worst start since 1982.