McNeese State's Kevin Hardy made two free throws with 12 seconds left, tying the game at 84, before Badillo's winner.
McNeese State (7-11, 1-6) made 20 of 30 first-half field goals and led 46-32 at the break.
Badillo had a 3-pointer and a three-point play, and Walker made two 3's, during a 14-6 run to open the second half which pulled Incarnate Word within 52-48.
A layup by Badillo gave the Cardinals an 80-79 advantage, their first since leading 7-6, with 2:58 left.
Desharick Guidry led the Cowboys, who shot a season-high 61 percent from the field, with 26 points.