Leon Clarke scored his ninth goal in four games to help the Blades to a Championship point.
Saturday evening's encounter was United's first draw in 26 games.
Despite the reversal in the nine-goal Fulham encounter in midweek, boss Wilder kept faith, selecting the same starting XI and substitutes.
The first 90 seconds were exclusively played in Birmingham's half as United started well but it took until 12 minutes to register the first chance, Clarke heading wide under pressure after patient build-up down the left.
At the other end Wright was called upon to make a timely tackle to halt Jutkiewicz latching on to Kieftenbeld's pass, but United were on top. Lundstram had two shots at goal in the space of three minutes but his first was blocked by Dean and goalkeeper Stockdale saved the second.
On 24 minutes Clarke shot wide after Fleck's cross, whilst, as the pressure mounted, Sharp was close to connecting with Basham's cross and Duffy was crowded out in the visiting penalty area.
United were then stung by a goal against the run of play. Jota's corner was half-cleared to the edge of the box where BOGA let fly with a 20-yard effort into the top corner. The goal stunned the Blades crowd and there was a chance for a second before the interval, from a break, but Wright made another great tackle to stop Jutkiewicz.
After a slow start to the second half, United began to force the visitors back. Fleck's drive from distance almost fell invitingly for Sharp and Lundstram was off-target with a first time effort from the edge of the box.
Carruthers and Brooks were introduced as boss Wilder changed the system but there was a nervous moment when a communication breakdown between Wright, Blackman and O'Connell saw Jutkiewicz gifted a chance but his shot was weak and easily cleared.
The striker was left to rue the opportunity as the Blades were level soon after. Yet another move down the left saw O'Connell feed Brooks, who laid off for CLARKE to beat Stockdale at his near post.
With the crowd revitalised, the Blades were now on the offensive. Duffy's pass resulted in Clarke being crowded out and from a corner routine Stevens almost wriggled free in the Birmingham box.
Late on former Blade Adams was introduced for the home side and quickly went on a mazy run, but Wright shepherded him wide enough for the threat to subside.
Carruthers had a shot blocked and O'Connell fired over before four added minutes was indicated. Injury-time saw just United trying to win but the visiting defence held firm to secure a point in front of the camera, with Morrison stopping Brooks in the box with the final action.
Blades: Blackman, Stevens, Fleck, O'Connell, Basham, Lundstram, Clarke, Sharp (Brooks 68), Wright, Carter-Vickers (Carruthers 68), Duffy.
Unused: Moore, Donaldson, Hanson, Stearman, Lafferty.
Birmingham: Stockdale, Nsue, Grounds, Roberts, Kieftenbeld, Jutkiewicz (Gallagher 90), Dean, Ndoye, Boga (Adams 86), Jota (Maghoma 78), Morrison.
Unused: Cotterill, Kuszczak, O'Keeffe, Gleeson.