The visitors took the lead in the 17th minute when Alan Judge's free-kick from distance found the net. Judge claimed the goal but Lee Hughes, attempting a glancing header, may have got a faint touch.
Ryan Flynn struck the equaliser in the 32nd minute, meeting Richard Cresswell's low cross with a fine half-volley at the near post.
Ched Evans and Matt Lowton both spurned good chances before the Blades found a winner on 51 minutes. Alan Sheehan, attempting to block Cresswell from connecting with Stephen Quinn's pass, could only shepherd the ball into his own net.
As United pressed, Stuart Nelson produced a fine save, turning Harry Maguire's header over while Evans fired against Stuart Nelson's right-hand post late on.
Jeff Hughes had a long-range effort well saved by Steve Simonsen and Karl Hawley volleyed straight at the Blades keeper from six yards.
And to add insult to injury, Magpies substitute Ishmel Demontagnac was sent off in stoppage time after throwing the ball at Lowton's face.
