Greenwood hit a 3-pointer to pull the Cowboys within one with 1:35 left and neither team scored until Potier found McFerrin for the winner.
Dexter Porchia missed the potential winning jumper for Dillard at the buzzer.
The Blue Devils shot 53 percent from the field, made 12 3-pointers and trailed for just 52 seconds.
Demetric Austin led Dillard with 23 points and eight rebounds. Dennis Hightower added 14 points and nine assists.
McNeese State had 11 steals and committed a season-low nine turnovers. The Cowboys made a season-high 12 3-pointers and made 31 of 62 field goals.