ACU, which has now lost 14 away games, led throughout the second half until Kevin Hardy made two free throws to tie the score at 80 with 16 seconds remaining.
ACU had a chance to seal the victory, but missed three consecutive free throws in the final 50 seconds of regulation.
McFerrin, who finished with 18 points, made four straight free throws to start the extra period for an 84-80 lead as the Cowboys (10-18, 8-8 Southland Conference) went on to take the win.
Ledrick Eackles, who finished with a career-high 35 points for McNeese State, fouled out with 50 seconds remaining in regulation. Parker Wentz, who led ACU with 24 points, fouled out with 1:51 left in overtime.
Julian Edmondson had 24 points for ACU (11-19, 2-11).