United's task was made easier when County's Gary Liddle was sent off after 13 minutes and they took the lead on the half-hour mark when Kevin McDonald charged into the box and volleyed home a cross from the right.
The visitors netted a surprise leveller just before the hour, when Enoch Showunmi sidefooted home from outside the area, but United's unmarked Harry Maguire headed in at the far post seven minutes later to wrap up the points.
Sheffield United's home ground, is the world's oldest professional football stadium, while Notts County, formed in 1862, are the oldest team in the world currently playing at a professional level.
The League One match was the first of six fixtures involving some of England's oldest clubs and venues to mark the Football League's anniversary.
(Reporting by Toby Davis in London; editing by Ken Ferris)
