Hawaii (11-3) took its first lead of the second half after three free throws with 53 seconds remaining. The Warriors made 6 of 8 free throws in the final minute to seal the comeback.
Isaac Fotu scored Hawaii's first seven points after halftime to pull Hawaii to within two-points. Fotu finished with 26 points.
Hawaii started just 1 of 10 from 3-point range but its next make cut the deficit to 58-54.
Two free throws by Caleb Steffensmeier gave Omaha its biggest lead of the game at 65-56 with 7:44 left. Hawaii responded with a 9-2 run to pull the Warriors within two.
John Karhoff led Omaha (10-5) with 15 points.
The first half was back-and-forth with seven ties and six lead changes.
Mike Brey is looking at former Notre Dame players to fill two assistant jobs that have opened up with the departures of Martin Ingelsby and Anthony Solomon.
Purdue's 2016-17 prospects got a jolt Wednesday when forward Caleb Swanigan announced he will return for his sophomore season.
Clemson's Jaron Blossomgame says he is withdrawing from the NBA draft and returning to school for a final season.