The game was Guidry's 12th double-double in 16 games this season.
McNeese State controlled the game with its defense and rebounding, holding Abilene Christian to 32.7 percent shooting while winning the rebounding battle by nine.
The Cowboys closed the first half on a 9-3 stretch and led 27-19 at halftime. The Wildcats would get within four late, but a layup by Hardy on a pass from Guidry put them away.
LaDarrien Williams scored 11 points to lead Abilene Christian (9-9, 3-2).
The Cowboys have won all five all-time meetings with the Wildcats.