After Omaha pulled to 70-67 with 52 seconds left, Wyoming dribbled down the clock and Justin James made a runner in the lane. Tre'Shawn Thurman answered with a 3-pointer with 13.9 seconds left for a two-point game.
McManamen hit two free throws to extend Wyoming's lead, but Jake White made a quick layup to make it 74-72 with 3.6 seconds left. Adams hit two free throws for a two-possession game and Devin Patterson hit a 3-pointer at the buzzer.
Adams finished with 31 points, his third 30-plus game this season, for Wyoming (7-4). He was 14 of 15 from the stripe. McManamen added 11 points and eight rebounds.
Thurman led Omaha (6-6) with 20 points and White had 17 points and 13 rebounds.