Rea's blow into the right-center field gap with two outs scored Alex Detz and Hunter Renfroe ahead of him, putting Mississippi State ahead.
Bulldogs closer Jonathan Holder struggled to hold the lead in the ninth, allowing a single and a walk. But he retired Danny Hayes on a long fly to end the game as Mississippi State advanced to Monday's winners bracket.
There they will play Indiana, which downed Louisville 2-0 in Saturday's late game.
Reliever Ross Mitchell earned the victory for Mississippi State.
Oregon State starter Andrew Moore yielded four runs on six hits over 7 1/3 innings.
Michael Conforto finished 4-for-4 with an RBI double for the Beavers, who will play Louisville in a Monday elimination contest.
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