City - who had Michael Keane sent off in the 26th minute for violent conduct - went behind 6 minutes before half time with defender Michael Byron deflecting the ball into his own net.
Jason Price levelled soon after the break, before Ashley Ward made it 2-1 to the Blades in the 71st minute.
But Price saved a draw 12 minutes from time with a header.
City line-up: Duke; Angus, Wiseman, Byron, Edge; Price, Fry, Keane, Anderson (Allanson 45); Walters, Facey.
Un-used subs: Benson, Donaldson, Cattermole, Beattie.