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The home run by Jones scored Wilbis Santiago to give the Hillcats (23-22) a 2-0 lead.
After Lynchburg added three runs, the Mudcats (28-19) cut into the deficit in the ninth inning when Pat McInerney hit a solo home run and Wes Rogers hit a sacrifice fly.
Lynchburg starter Matt Solter (3-0) picked up the win after allowing five hits over 5 2/3 scoreless innings. Opposing starter Nelson Hernandez (5-2) took the loss in the Carolina League game after giving up five runs and four hits over six innings.
The Mudcats, 3 1/2 games back of the Down East Wood Ducks in the Carolina League's Southern Division, begin a four-game series with the Kinston club Friday at Five County Stadium.