United fought back twice to protect their proud unbeaten away record, which stood at 12 games after the 2-2 stalemate with Plymouth Argyle in February 2009.
Danny Webber and Greg Halford cancelled out goals from Carl Fletcher and Paul Gallagher, all in the second-half, on a testing Home Park pitch.
Craig Beattie made his Blades debut from the bench in front of 668 Unitedites, who braved the elements in the West Country.
Plymouth: Larrieu, Duguid, Gallagher (Noone 87), Fallon, Barker, Sawyer, Cathcart, Judge (Paterson 73), Mackie (Barnes 87), Fletcher, Gray.
Unused: Timar, MacLean.
Blades: Kenny, Halford, Naysmith, Cotterill, Morgan, Kilgallon (Bromby 75), Lupoli (Beattie 55), Webber (Ward 73), Montgomery, Quinn, Naughton.
Unused: Hendrie, Sharp.
Attendance: 10,044
Referee: A Woolmer