Kaleb Cowart put Cook on top with a two-run homerun in the first and the Hornets added two more in the second.
Palmer Betts allowed one run through six innings.
He was lifted after giving up a two-run homerun in the top of the seventh.
Mercer signee D.J. Johnson got the final three outs.
Cook, a number one seed, will host #2 seed Blessed Trinity in the AA quarterfinals on Monday.
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