Illinois State set up a second-round meeting with Stanford in an entertaining contest that saw Illinois State convert 17-of-23 shots from 3-point range.
Moore hit one of those long shots with 2:26 left in the extra period to give the Redbirds a seven-point advantage.
Illinois State scored the final point in regulation when Anthony Cousin hit a free throw with 7 seconds to play.
Tyler Brown scored 26 points for Illinois State (21-13), which lost an overtime thriller to Creighton in the finals of the Missouri Valley Conference Tournament. Moore, who went 6-of-6 from 3-point range, added 25 points Wednesday.
Mississippi (20-14) got 25 points from LaDarius White, who made 10-of-12 shots from the field.