The win puts the Monarchs (27-7) into the semifinals at Madison Square Garden for the first time since 2006.
After trailing for the entire game, Jeffery Moss hit a 3-pointer for the Racers with 3.5 seconds left to tie it at 69. Freeman took the inbounds pass and dribbled up the right side under heavy pressure, launching his 35-foot runner just before the horn.
Freeman, a junior guard, scored 25 points. The Monarchs' leading scorer missed most of ODU's second-round victory over Illinois State with an ankle injury.
ODU took a 10-point lead with 3:39 to play but the Racers used a 14-4 run — capped by Moss' 3 — to tie it.
Cameron Payne led Murray State (29-6) with 23 points.