Obi Emegano, who entered play seventh in nation in scoring average at 22.7 points, led Oral Roberts (11-11, 3-5 Summit) with 29 points.
Omaha led by nine at the break, 46-37, but Oral Roberts clawed back to take a 72-71 lead on Jalen Bradley's 3-pointer with 4:34 to go.
Omaha took the lead back on Patterson's layup, then a pair from the line by Hollins. Emegano made 5 of 6 from the line late - the last to keep Oral Roberts within two points with 39 seconds - but the Golden Eagles didn't score again.
Hollins hit a jumper with 19 seconds left, and then Patterson made two free throws to seal it.