Ethan Ebanks-Landell netted a dramatic equaliser in the final minute of added time to earn United a point and extended the unbeaten run.
It was the loan defender's mistake that added Fleetwood a first half lead, but he atoned in front of 1,361 ecstatic Blades fans.
For the trip to the north west, defender Wright returned to the starting line-up, replacing Scougall, who dropped to the bench after suffering with illness in midweek. Lavery was ruled out after tweaking ankle ligaments in midweek.
United reverted to three central defenders on a slippery, heavily-watered surface and the brighter start came from the visitors, which included a fantastic opportunity to take the lead on three minutes. Fleck threaded a ball through the defence to put Done in the clear but goalkeeper Neal blocked with his body.
Coutts also had a shot deflected wide, whilst United's high press caused Fleetwood a few problems, but the home side were gifted the lead on 13 minutes. Ebanks-Landell's attempted back-pass was cut out by Long and although his shot was kicked off the line by Wright, the loose ball dropped to BALL to slide into an unguarded net.
United looked to respond with a deft Sharp chip on the turn, which was pushed over the crossbar, and from the resulting corner, O'Connell's header was scrambled clear.
The action was thick and fast, at both ends. Moore was forced to save from Ball and Dempsey, whilst a Lafferty break set up a chance for Sharp, but Neal kicked away the skipper's shot.
As half-time approached it was United on top and getting around the back of the home defence frequently but that final pass proved elusive and Fleetwood held their slight advantage at the break, just, after Lafferty headed wide a Done cross with the last action of the half.
United began the second half on top but Fleetwood created the first chance, Moore saved from Long and Grant sent the rebound over the top. For the Blades, Sharp got the better of Pond but the subsequent Fleck shot was saved by Neal's legs.
Wilder made two changes before the hour, also altering the shape, and used his final one, introducing Chapman, with a quarter of the game to go.
With Fleetwood trying to frustrate and slow the game down at every opportunity, United continued to try and force the issue. From Hussey's cross, Done headed wide at the back post and Chapman cut in before shooting wide.
On 82 minutes, Hussey's cross was turned onto the outside of his own post by Pond, whilst on the break, Hunter went close to doubling the lead with a header but Moore made a tremendous reaction save.
Fleetwood used every trick in the book to slow down the action, helping towards five minutes of added time. Chapman's shot was deflected wide, whilst Sharp was crowded out as he looked to shoot.
The late action was frantic and Freeman's header caused problems in the box but when Fleetwood thought they had survived, they hadn't!
One final cross from Hussey saw EBANKS-LANDELL, added to the attack, rise highest and direct a header into the bottom corner, out of the reach of Neal, who was moments later named man of the match!
There was just time to kick-off before the referee signalled full-time.
Fleetwood: Neal, McLaughlin, Bell, Eastham, Pond, Ryan (Woolford 60), Ball (Hunter 66), Grant, Duckworth, Long (Jonsson 76), Dempsey.
Unused: Bolger, Cairns, Cole, Jakubiak.
Blades: Moore, Fleck, O'Connell, Sharp, Done, Wright (Scougall 58), Coutts, Freeman, Ebanks-Landell, Duffy (Chapman 67), Lafferty (Hussey 52).
Unused: Ramsdale, Brown, Wilson, Whiteman.