The Bearkats (3-2) trailed 51-48 with 9:36 left in the second half after a layup by Oral Roberts' Damen Bell-Holter and Kryon Stokes' jumper. Sam Houston State answered with 11 straight points, led by Allmond's 11 points during the run to pull ahead 59-51.
Kevin Ford's layup cut the margin to one point with 42 seconds left for the Golden Eagles (2-3). But the Bearkats secured the victory as Preston Brown followed with a three-point play and Lance Pevehouse added two free throws down the stretch.
Sam Houston State, which shot 28-for-56 from the floor, scored 21 points off of Oral Roberts' 17 turnovers.
Michael Craion led Oral Roberts with 14 points and 10 rebounds.