Eastern Illinois (13-9, 7-3 Ohio Valley) led 55-54 after Anderson's free throw and pressured SIU-Edwardsville's Donivine Stewart into a turnover with 4.8 seconds left. Cornell Johnston made two more free throws with 2.4 seconds.
Kris Davis missed off the rim from half court at the buzzer.
Anderson had 20 points, helping the Panthers to snap a three-game skid. Johnston added 12 points.
Stewart was 5 for 7 from 3-point range and finished with 19 points, eight rebounds and six assists. Keaton Jackson grabbed a career-high 15 boards.
Neither team led by more than four after SIUE tied it at 28-all early in the second half.