United were forced to settle for a point at St Andrews on Wednesday evening.
Enda Stevens fired the Blades in front, but Michael Morrison quickly restored parity for the hosts just before the interval.
For the clash in the midlands, boss Wilder made just one change from the starting XI that won at Preston at the weekend. Cranie replaced Dowell, who dropped to the bench, where he was joined by the returning Madine.
On four minutes United had the first chance, but Sharp was offside from Norwood's free-kick, after Pedersen had fouled Baldock. United were on the front foot again moments later, but after some good build-up play, Sharp was just unable to pick out McGoldrick in the box.
United had a scare on 19 minutes though as Gardner broke free down the right, his low cross took a wicked deflection off Cranie, but Henderson managed to claw the ball, despite colliding with the post. The hosts had now got a foot hold in the contest and Dean lashed over from a promising position after the Blades failed to clear.
Just after the half hour, Davis was booked having caught Norwood late on halfway. And in the 38th minute, United went in front. Duffy was involved in the build-up, but it was STEVENS who fired home, beating Camp for pace at his near post. The advantage lasted only four minutes though, as MORRISON forced the ball home on the rebound, after Gardner's header had been saved on the line.
The first real opportunity of the second-half came from another Norwood free-kick. McGoldrick found space at the back post, but Camp was equal to his low effort. On the hour, Wilder made a double change, with Madine and Dowell replacing Duffy and Cranie.
City broke quickly and Jota fed the run of Adams, but Henderson was at his agile best to deny the former Blade. Another break from the home side, saw Adams get the better of Egan, but Jota was denied by Henderson. United responded by getting on the front foot and Sharp drew a foul from Morrison that resulted in a booking for the Birmingham captain.
The game was visibly opening up with 20 minutes remaining and from Basham's cross, McGoldrick flashed a header across the face of goal. United were now the ones forcing the issue, with Basham a threat offensively, but Dean hacked the ball away for a corner, with Sharp ready to pounce.
With the clocking ticking down, United poured forward in search of a winner and McGoldrick's header was inches away from hitting the back of the net, from Norwood's corner. Three minutes of added time were signalled and Egan's header was saved by Camp, as United had to settle for a share of the spoils.
Birmingham: Camp, Colin, Morrison, Dean, Pedersen, G Gardner, Davis (C. Gardner 83) Maghoma, Mahoney (Jota 60), Adams, Jutkiewicz.
Unused: Trueman, Harding, Roberts, Mrabti, Craig, Vassell.
Blades: Henderson, Baldock, Stevens, Fleck, Basham, Sharp, Egan, Norwood, McGoldrick, Duffy (Madine 60), Cranie (Dowell 60).
Unused: Hogan, Coutts, Freeman, Stearman, Moore.