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The home run by Wilson capped a four-run inning and gave the Red Sox a 9-6 lead after Garrett Benge hit an RBI single earlier in the inning.
In the bottom of the ninth, Carolina cut into the deficit on a solo home run by Ryan Aguilar.
Robbie Baker (2-1) got the win in relief while Justin Topa (0-1) took the loss.
Mario Feliciano homered and singled, scoring a couple of runs while also driving home two for the Mudcats.
The series continues Friday.