Dantrell Thomas missed a layup with a second left that would have tied the game.
Incarnate Word (20-6, 8-5 Southland Conference) held a 32-22 lead at the half and led 62-47 with 4:41 remaining.
The Cardinals, who hit 9 of 20 from beyond the arc, shot 48.1 percent from the field.
Sam Burmeister led the Cardinals with 18 points, Kyle Hittle and Denzel Livingston had 13 apiece and Anthony Horton added 11 for the Cardinals.
Smith had 18 points and Sam McBeath added 12 for (12-13, 9-7).