Pawel Abbott took just 10 minutes to give the Quakers the lead before a Gregg Blundell header wrapped up the points after 76 minutes.
Shrewsbury find themselves in third position in the table after they were held to a 1-1 draw by Stockport. Dave Hibbert gave the Shrews a 25th-minute lead but Adam Proudlock cancelled the goal out seven minutes later for County.
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