United's first draw of the season was the outcome on a frustrating night at Bramall Lane.
The scoreline didn't tell the full story of what was an end-to-end game though, with both teams having numerous chances to snatch all three points.
For the clash against the Blues, Wilder opted to freshen his side up, with Johnson and Washington handed full debuts. Baldock, Fleck and Clarke also returned to the starting XI.
United were on top in the open 20 minutes, without troubling Camp, but Norwood's free-kick from wide on the right almost caught the goalkeeper out, after Pederson had upended Baldock. Moments later, Fleck whipped in an inviting centre from the left which just evaded Washington who was under pressure from Dean.
It was the Blades who continued to make the running, with Camp just about keeping out Duffy's deflected effort at the expense of a corner, from which O'Connell headed wide. In response, Jutkiewicz powered forward holding off two challenges before a combination of Henderson and the post kept his effort at bay.
Within two minutes of the restart, the Blades had their best chance of the night, Lakin surrendered possession in his own half and Norwood instantly played in Baldock, who was denied was a combination of Camp and Morrison.
In United's next attack, Egan had a headed save by Camp, but referee Ward had already blown for a foul by the Irishman.
United's first change just after the hour saw McGoldrick introduced replacing Washington, who received a warm hand for his efforts. And McGoldrick nearly made an immediate impact, shooting wide after Fleck had got the better of Lakin. The visitors responded with a quick break and from Colin's cross Adams saw a diving header saved by Henderson.
Sharp and Woodburn took the places of Clarke and Duffy as United chased a winner. But on 80 minutes, the Blades had a let off, Jota's deep cross found Jutkiewicz at the back post, but Bogle turned the ball over with the goal at his mercy. The Blues came even close moments later, as Gardner hit the post with a powerfully struck free-kick.
United pressed forward, but were nearly caught on the break. Jota advanced and freed Mahoney, but Henderson made himself big to save at the expense of a corner. Four minutes of added time were signalled, and O'Connell's booking was the last meaningful action of the night.
Blades: Henderson, Baldock, Fleck, O'Connell, Basham, Clarke (Sharp 70), Egan, Norwood, Duffy (Duffy 77), Johnson, Washington (McGoldrick 61).
Unused: Stevens, Lundstram, Stearman, Moore.
Birmingham: Camp, Pederson, Colin, Adams (Bogle 70), Jutkiewicz, Dean, Maghoma (Mahoney 78), Gardner, Jota, Morrison, Lakin (Harding 89).
Unused: Roberts, Solomon-Otabor, Trueman, Lubala.