Halter's two-out grounder up the middle scored Justin Foscue just after 3 a.m. CDT on Thursday morning to end the marathon after 6 hours, 43 minutes.
With one out, Foscue struck out but reached first base on a wild pitch. He also advanced to second on a wild pitch.
Mississippi State (46-11) jumped out to a 4-0 lead in the first three innings, but failed to capitalize on opportunities to extend the margin. The Tigers rallied with four runs, including Giovanni DiGiacomo's two-run homer in the eighth that tied it.
The teams traded runs in the 16th before Halter's hit won it in 17.
LSU had a great chance to close it out in the 16th, but second baseman Brandt Broussard misplayed a grounder with two outs, allowing Rowdey Jordan to score the tying run.
The game featured an impressive duel between bullpens. Matthew Beck and Zack Hess both threw four scoreless innings for LSU. Cole Gordon countered with five shutout innings for Mississippi State.
Mississippi State will play Vanderbilt on Thursday. LSU (35-23) will face Auburn in an elimination game.
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