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The sacrifice fly by Silva capped a two-run inning and gave the Mudcats (15-10) a 4-3 lead after Pat McInerney hit an RBI double earlier in the inning.
The Mudcats, who won their third straight contest, tacked on another run in the seventh when Rob Henry hit a solo home run.
Cody Beckman (2-0) got the win with three innings of scoreless, two-hit relief while Alex Demchak (0-1) took the loss in the Carolina League game.
Jarren Duran tripled, doubled and singled for the Red Sox (11-13). Pedro Castellanos doubled twice and singled, driving home two runs.