The Panthers (9-18, 5-13 Ohio Valley) raced out to a 20-4 lead in the opening 11 minutes of the game and never trailed from there. Martin and Byrne combined for 10 points during the run.
Roderick Pearson scored 17 points to lead Southeast Missouri (10-17, 8-10).
Eastern Illinois shot nearly 58 percent in the opening 20 minutes and better than 52 percent for the game. The Redhawks shot 26 percent in the first half and 35 percent overall while converting just 8-of-28 3-pointers.
The Redhawks trailed by double figures for most of the second half before cutting the Panther lead to seven with 31 seconds left. Robinson then made two free throws to seal the outcome.