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The Blades went ahead after 16 minutes when Harry Maguire played in Stephen Quinn, who turned unchallenged to finish from just inside the box.
Top scorer Ched Evans extended the lead after 22 minutes when he finished from a tight angle and the Blades were threatening to run riot on five minutes later as Matthew Lowton fired home a stunning 30-yard shot.
A terrible first half for the home side was completed on the stroke of half-time as a quick corner saw Kevin McDonald cross for Neill Collins to head home to make it 4-0.
In the second half, a perfectly-placed free-kick from Alan Judge gave County hope after 77 minutes but Notts skipper Neal Bishop saw red for a second bookable offence three minutes afterwards.
Lee Williamson completed the Blades' scoring in the 89th minute with a cool finish before substitute Julian Kelly nodded home a second consolation goal for Keith Curle's side.
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