Jackson State (18-13) built an early comfortable lead, but the Lady Panthers (22-11) went on a 7-0 spurt to tie the game at 38-38 when tournament MVP Trahan briefly went down with an apparent ankle injury.
Prairie View grabbed its first lead with 11:32 remaining on a layup by Dominique Smith, setting off a back-and-forth flurry in which there were six lead changes.
But the Tigers survived that exchange and a flurry of desperation 3s by the Panthers to earn the automatic bid.
Shavonne Smith scored 18 points and Chari Smith added 13 for Prairie View, which was without All-SWAC performer Gaati Werema who sprained her knee in the semifinals.
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