The game was tied at 77 with 1:00 remaining after Houston Baptist's (6-25, 2-16 Southland) Marcel Smith drilled a 3-pointer. Cody Joyce fouled Desharick Guidry on the next possession, and Guidry hit 1 of 2 to give McNeese State (11-19, 9-9 Southland) a one-point lead with 46 seconds left.
HBU's Rob Lewis missed a layup and moments later fouled Eackles, who hit 1 of 2 and the Cowboys led by two.
Colton Lasher's 3-point attempt missed, and Brandon Regis hauled in the rebound to ice the Cowboys' win.
McNeese State was up nine early, but Houston Baptist used a 12-0 run - including two 3-pointers by Tyler Russell - to lead 37-31 at halftime.
Craig McFerrin and Kevin Hardy both had 16 for McNeese.
Lasher led Houston Baptist with 13.