Wright State jumped out to a 3-0 lead after four innings on home runs by Conlan Daniel and Boston Smith.
But the game changed after Wright State pulled starter Cam Allen, who had a no-hitter through six innings.
Brodie Johnston broke up the no-hitter with his team-high 14th home run of the season over the left-field wall leading off the seventh.
Mike Mancini hit his fourth home run of the season in the eighth, just over a leaping attempt by center fielder Smith.
Nelson’s deep shot over the pole in right field was initially called foul before it was over overturned on the field. Wright State’s challenge was unsuccessful.
Vanderbilt (43-16) will look for its 10th straight victory on Saturday against Louisville in the winner's bracket. Wright State (38-20) faces East Tennessee State in a loser-out game.
Thompson (6-5) retired 15 of 16 batters after Smith's homer in the fourth. Sawyer Hawks struck out the side in the ninth for his eighth save.
Warren Hartzell (6-3) allowed all four runs for Wright State, which last won a NCAA Tournament game in 2016.
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