The victory sends the Golden Eagles into a quarterfinal matchup with No. 3 Sam Houston (21-9).
Oral Roberts (17-15) lost its regular-season meeting with the Cowboys, falling 79-68 at Lake Charles in February when its 13-point first-half lead evaporated in the second half.
McNeese State (11-20) pulled within three points on a 3-pointer by Ledrick Eackles with 1:22 left and again on an Eackles 3 with 5 seconds left. Glover responded to the first trey by hitting jumper and Bobby Word added a pair of free throws. Billbury answered the second 3-pointer by hitting the first of two free throws.
Billbury finished with 18 points for Oral Roberts, with Glover adding 17.
Eackles led the Cowboys with 28 points.