McNeese led by three in overtime with just under 1 minute remaining, but Nicholls State (7-10, 10-4 Southland Conference) scored seven straight points as Dominic Friend and Anatoly Bose hit back-to-back 3-pointers and Chris Iles hit a free throw.
The Colonels, who were 4-for-4 from long range in overtime, were 53.3 percent on 3-pointers in the game (16 of 30).
Bose tallied 16 points and Iles added 12 points and a career-high five assists for the Colonels.
Nicholls State led 62-53 with under 4 minutes to play in regulation, before the Cowboys (11-16, 5-9) went on a 13-4 run, capped by a 3-pointer from Patrick Richard with 3 seconds to go to send the game to overtime.
Richard led McNeese State with 24 points.