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Carolina (19-14) started the scoring in the first inning. After leading off the inning with a single, Joantgel Segovia advanced to second on a walk by Ryan Aguilar and then scored on an error.
The Woodpeckers took the lead for good with three runs in the third inning. Sierra hit a solo home run en route to the two-run lead.
The Woodpeckers tacked on another run in the fourth when Seth Beer hit an RBI single, driving in Bryan De La Cruz.
Carolina saw its comeback attempt come up short after Aguilar scored on a groundout in the eighth inning to cut the Fayetteville lead to 4-2.
Fayetteville right-hander Enoli Paredes (2-1) picked up the win after allowing one run on four hits over five innings. Opposing starter Matt Smith (1-3) took the loss in the Carolina League game after allowing three runs and five hits over 2 2/3 innings.
Eddie Silva doubled and singled, also stealing a base for the Mudcats.
The Mudcats remain home Friday to face the Myrtle Beach Pelicans at 7 p.m.