United hit back from 3-0 down to earn what could prove to be a vital point against fellow promotion contenders Wigan Athletic.
Goals from Will Grigg, Haris Vuckic and Chris McCann gave Wigan what looked an unassailable lead with little more than 20 minutes remaining.
But two close-range Matt Done goals and a Billy Sharp header gave the Blades a point and late on it was the visitors on the offensive.
Wigan old boy Adkins made three changes for the DW Stadium encounter. Done, Baxter and Flynn returned; Sammon and Woolford dropped to the bench and Coutts was rested.
Collins headed over the first opportunity from a Baxter free-kick, whilst Wigan won a couple of early corners and there was a shout for a penalty when a cross from Jacobs hit Brayford. On 11 minutes, Jacobs also forced a save out of Long at the near post.
Twice in the same move Wigan failed to clear their lines but Basham's cross was repelled and Sharp curled over before the home side took the lead, with more than a little help from referee Woolmer. On 16 minutes, McEveley's pass was ideal to put Flynn in space but the ball hit the referee's heels and dropped kindly for Jacobs to play in GRIGG, who duly beat Long.
A minute later the officials made a clear error when Long saved from Grigg, who threatened to make it 2-0 but a goal-kick was the decision. With both sides making mistakes on a slippery surface, Long made another save from Grigg after Edgar lost out to combination of the goalscorer and McCann.
Neither side could claim to be clearly on top but United were denied a great chance to level on 40 minutes. Sharp's pass put Baxter in the clear but he was hauled down on the edge of the box by Daniels. Fellow Wigan players in the vicinity gave referee Woolmer the chance to show the defender a yellow card but it could be argued the pace Baxter was moving, the card could have been red.
Baxter fired the free-kick over and the misery was compounded as Wigan netted a second with their next move, the last one of the half. On 43 minutes, Perkins and Jacobs were both involved before a Pearce cross from the left was deftly flicked home by VUCKIC in a crowded penalty area.
Early in the second half, Wigan had opportunities to extend their lead but Pearce headed over from a corner and Vuckic missed the target after Basham gave away possession.
United hit back. From Sharp's cross Flynn's effort was deflected wide and referee Woolmer ignored claims for a penalty when Done was held from Baxter's cross.
Just after the hour there was a great chance to reduce the arrears but an unmarked Sharp could not hit the target from Brayford's cross and Wigan took advantage to net a third soon after. There appeared to be plenty of green shirts in the box but a shot from Daniels was saved by Long, although from the follow up from McCANN's effort crept between the goalkeeper's legs.
There was a bit of hope within two minutes as United pulled on back. Sharp's cross looked to be behind DONE, but he curled his leg around the ball and placed into the corner.
Basham then had a shot blocked before United claimed a second. McEveley beat Daniels on the left and his deflected cross was ideal for SHARP to nod past Jaaskelainen from close range.
Adams and Woolford were introduced and the Blades went in search of an equaliser, although holes appeared at the back - Grigg and Power had chances to extend the lead.
Done turned in a Hammond side-foot but the flag had already been raised for offside, but he was not to be denied! The clock was ticking around to 89 minutes when, after Cowie gave away the ball, Jaaskelainen could only parry Sharp's shot and DONE poked home the rebound.
After the Blades had done celebrating, six minutes of added time was announced and it was the visitors pushing. Jaaskelainen made a better fist of saving from Sharp from 20 yards and Done sliced wide before the final whistle.
Wigan: Jaaskelainen, Perkins (Cowie 65), Daniels, Power, McCann, Grigg, Jacobs, Morgan, Barnett (James 80), Pearce, Vuckic (Wildschut 62).
Unused: Nicholls, Kellett, Davies, Hiwula.
Blades: Long, Brayford, Basham, Flynn (Adams 77), Sharp, Baxter, Done, Collins, McEveley (Woolford 77), Edgar, Hammond (Campbell-Ryce 88).
Unused: Howard, Sammon, Reed, McGahey.