Melvin Morgan, who led the Bengals with 15 points, made a jumper which gave Idaho State its largest lead in the second half at 31-22.
Utah (2-1), which got 11 points from Glen Dean, began bypassing outside shots and started to find Bachynski inside. The 7-footer powered a 15-1 run that culminated in Jason Washburn's layup for a 54-38 Utah edge with 6:26 to play.
After surrendering a late 13-point lead to Sacramento State last Friday to lose 74-71, the Utes again struggled on offense down the stretch. Bachynski missed two dunks late in the final minutes but Idaho State (0-3) couldn't convert on the other end, missing four 3-pointers on a single possession in the final minute.
The Utes next host Central Michigan Friday at 5:00 p.m.