James Beattie took his scoring tally to six as a calamitous goalkeeping error gifted United a draw after another abject away performance.
Paul Rachubka allowed a speculative long-range Beattie strike to slip through his fingers in the closing minutes at the seaside to gift United a first away point.
Beattie had given United the lead but Blackpool levelled on the stroke of half-time through a Stephen Crainey free-kick. The home side were on top in the second half and had a good shout for a penalty turned down before Ben Burgess headed them in front after 87 minutes.
The Blackpool fans were still celebrating as they watched their goalkeeper's error deny them a win and 1,852 uncovered Blades supporters knew they were fortunate to be taking home a point.
For the trip to a windy Bloomfield Road, boss Robson made just one change from the team that defeated Wolves at the weekend. Stead was rewarded for his injury-time goal with a starting berth in place of Webber.
In a very entertaining opening, both sides worked two chances each in the first five minutes. United were the first to show, Bromby cracking a 30-yard shot into the arms of Rachubka with just 49 seconds gone, whilst before another minute had elapsed Fox fired over for the home team.
On four minutes Blackpool put together a decent move which ended with Taylor-Fletcher wasting a great chance at the back post from Crainey's delivery and then, for United, Quinn's drilled effort was well off target but was deflected by Barker and forced goalkeeper Rachubka into a reaction save.
United, however, found the opening goal on 13 minutes and it came from a familiar source. A delivery down the left channel by Naysmith found Stead, who held off his man and crossed for BEATTIE to beat the wrong-footed Rachubka with a downward header from six yards.
The visitors attempted a similar manoeuvre moments later, albeit from the right. This time Beattie delivered and Quinn, attacking from his left flank position, headed over.
With Hoolahan looking a threat on the left, Blackpool went back on the attack but the home side's next chance came from the opposite flank. Barker's cross looped up off Naysmith and Kenny had to be well-placed to tip the swirling ball over.
Barker's long throw would have been highlighted as a dangerous weapon before the game and on 34 minutes that proved to be the case. The launch down the right was flicked inside by Burgess and United were thankful that Taylor-Fletcher snatched his shot wide from the edge of the box.
On 39 minutes the Blackpool strikers caused United trouble when Morrell edged on and Burgess held the ball up before curling wide from 20 yards. The effort was close, as demonstrated by Kenny's full-length dive.
United hit back but Bromby's header into the ground was comfortable for Rachubka following a Quinn cross and the first half work was undone on the stroke of the break.
The referee's watch had just ticked around to 45 minutes when Morgan was pulled up for a foul on Morrell on the edge of the box. The Blades skipper argued his case but Mr Halsey had made his decision and CRAINEY lined up the free-kick before curling over the wall and into the corner of the net.
There was just time for the referee to re-start the game before signalling for the break and it was the home team that skipped off for their half-time cuppa the happier.
Blackpool wheeled out two former Tangerine and Blades players to make the half-time draw. The introduction of Alan Wright and John Burridge brought a warm round of applause before the current players re-emerged.
Despite a lack of goalmouth action early in the second half the home fans were vociferous in their backing of Grayson's team, whilst Robson gave Carney his first taste of Championship action at the expense of Quinn.
Blackpool began the second period the better, enjoying the majority of possession, and had Hoolahan shown a better first touch after Taylor-Fetcher's pass he could have seriously tested Kenny on 56 minutes.
Robson made his second change on 65 minutes, the elder Quinn replacing Gillespie, and just 60 seconds later the Blades could have fell behind had Mr Halsey shown a bit of consistency. Blackpool's earlier goal was the result of a Morgan high challenge on Morrell and when the same duo clashed again the referee waved play on, despite the Blades skipper's foot being higher and actually catching the striker on the head as he attempted an unorthodox clearance.
The home side continued on the offensive, despite Robson throwing on a third striker in Webber. On 69 minutes Morrell broke the offside trap and played in Taylor-Fletcher but the subsequent shot was saved by Kenny low to his left and then Morgan hooked on the ball onto the top of his own netting as United defended frantically.
It was the 78th minute before the Blades created a chance in the second half. Armstrong lost possession but won the ball back from Hoolahan before striking a low shot just wide of Rachubka's left post, then Carney hit a speculative volley wide.
The game warmed up in the last five minutes, beginning with Carney's run which saw his deflected cross find Quinn but the substitute fired just wide.
Blackpool's pressure finally paid off on 87 minutes when they netted what they thought was the winner. From substitute Welsh's inswinging cross, BURGESS lost his marker and beat Kenny with a header from six yards.
However, the game was not over and a combination of the wind and Rachubka taking his eye off the ball handed United a share of the points. BEATTIE tried his luck from all of 30 yards and the goalkeeper made a total mess of the effort and the ball trickled over the line.
Three minutes of added time failed to add to extra drama and the United camp breathed a huge sigh of relief at the final whistle.
Blackpool: Rachubka, Crainey, Southern, Jackson, Evatt, Morrell (Parker 85), Hoolahan, Taylor-Fletcher (Welsh 82), Fox, Barker, Burgess.
Unused: Coid, Vernon, Gorkss.
Blades: Kenny, Bromby, Naysmith, Morgan, Beattie, Stead, Kilgallon, Tonge (Webber 73), Gillespie (A. Quinn 65, Armstrong, S. Quinn (Carney 54).
Unused: Lucketti, Sharp.
