Johnston was 7 of 7 from the field, including four 3-pointers, and hit both of his free throws. Anderson made 7 of 10 shots.
Eastern Illinois (15-10, 8-4 Ohio Valley) had 19 assists on 25 field goals and connected on 56.8 percent of its field goals.
Johnston scored 10 of Eastern Illinois' first 14 points of the game. He had 15 points in the opening 20 minutes as the Panthers led 39-31.
Eastern Illinois only made one field goal in the first eight minutes of the second half and Austin Peay tied the game at 41 at the 11:38 mark. But the Panthers answered with an 8-2 run and later, Anderson converted consecutive three-point plays for a 66-52 lead.
Chris Freeman had 20 for Austin Peay (7-18, 2-9).