McNeese State (10-10, 6-2) shot 56 percent from the field (24-of-43) with three players in double figures as Dontae Cannon added 12 points.
Sam Houston (8-14, 2-6) was led by Demarcus Gatlin and Marcus James, both with 16 points.
The Bearkats jumped out to an early lead, going up 19-11 with 12:31 to play in the first half. McNeese State roared back, out-scoring the Kats 30-11 in the final 12 minutes of the first half to go up 41-30 at intermission.
Sam Houston cut the margin to two points, 63-61, after a pair of free throws by Demarcus Gatlin with 2:30 to play. But Mitchell hit a jumper with 1:17 left and Richard added a pair of free throws with 0:28 to go to put the game out of reach.
McNeese was consistent the entire way, shooting 55.8 percent from the field on the night and 88 percent from the free-throw line.
McNeese also capitalized on nine Sam Houston first half turnovers for 18 points.
Sam Houston took a 19-11 lead on a jumper by senior Marcus James. Then the Cowboys got rolling. McNeese went on a 21-2 run and took a 41-30 lead into halftime.
Even though Sam Houston shot nearly 53 percent from the field in the first period, that eight-minute stretch where the Bearkats scored just two points and turned the ball over six times left them playing catch-up against the Southland Conference East Division's strongest team.
Sam Houston travels to Hammond, La., on Saturday to start the back end of the conference schedule against Southeastern Louisiana, one of two teams the Kats are tied with for the eighth and final postseason spot.