Sam Sheridan scored a late winner for Stockport after Barrow had battled back from 2-0 down as County won for the first time in 13 matches.
Sheridan's 25-yard volley put the hosts ahead before Joe Connor scored his first senior goal with a tap-in after Aaron Cole's shot had been parried.
Richie Baker headed a goal back for Barrow and then converted a penalty following Daniel O'Donnell's handball.
But Sheridan won it from the spot after Paul Smith had brought down Cole.
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