Goals from James McAtee and Iliman Ndiaye had United seemingly in control of the game, before Jerry Yates dragged the visitors on level terms before the break.
Charlie Patino put them ahead in the second half but the visitors had both Marvin Ekpiteta and Dominic Thompson sent off for two yellow cards.
United had two goals chalked off for offside and missed a penalty before eventually finding the equaliser deep into eight minutes of injury time, Ollie Norwood volleying home from outside the area.
There was still time for one more excellent Blackpool chance, former Blade CJ Hamilton racing clear before failing to get good connection on his shot, and both Wes Foderingham and Shayne Lavery were shown red cards after the final whistle after a coming-together at full-time.
Here’s how we tried our best to rate United’s players on an up-and-down afternoon full of late drama at the Lane...
5. Rhys Norrington-Davies 4
Too easily beaten down the Blackpool right by Lavery, who then crossed for Yates to drag Blackpool level at 2-2. Seemed to lack a little of his usual confidence and tenacity going forward and ballooned a late cross out of play with United pushing for a goal. Photo: Isaac Parkin
6. Ben Osborn 4
Made a first start since May's play-off semi-final against his old club Forest and couldn't do enough to prevent Yates heading home in the first half from a corner. Not apparent if he was meant to mark the striker but Yates took advantage at a key moment. Made way for McBurnie as United looked to get back in the game Photo: Isaac Parkin
7. Ollie Norwood 8
In the right place at the right time to poke the ball away from former teammate Madine as he looked to drag the visitors level in the first half. Superb ball down the line led to Brewster's run which saw Ekpiteta sent off and almost led to the equaliser, but Egan hit the side-netting from Norwood's wicked free-kick. Great vision to pick out McBurnie late on but his header was well saved. Then came up with the equaliser when it mattered Photo: Simon Bellis
8. Tommy Doyle 6
He, and the Kop, thought he had put United ahead early on but the flag had already gone up with Sharp straying offside. Almost put the Blades 3-1 ahead with a rasping drive that Maxwell did brilliantly to palm over the bar Photo: Isaac Parkin