Shawn Glover scored 17 points and Brandon Conley added 11 for the sixth-seeded Golden Eagles (17-15). They will face third-seed Sam Houston State in the next round.
Ledrick Eackles finished with 28 points on 6-of-21 shooting for the seventh- seeded Cowboys (11-20).
Oral Roberts shot 36.7 percent from the field, including 3-of-12 from beyond the arc, in the opening frame as it led 28-24 at the half. McNeese State struggled and made just 22.6 percent of its field goal tries.
The Golden Eagles played better in the second half as they connected on 48.1 percent from the floor. OThe Cowboys cut their deficit down to three in the second half, but never led, shooting 33.3 percent over the final 20 minutes.
Oral Roberts converted on 42.1 percent of its shots from the field in the win, and McNeese State did much worse making just 28.1 percent.