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...
9. James McAtee 6
Looking to build on his assist and positive display last time out at Stoke, McAtee's nice pass slipped in Sharp early on but he was offside and Doyle's goal was ruled out. The opener did come, though, when McAtee bundled home in front of the Kop for his first goal in senior football. Booked for diving late in the first half and replays suggested that if there was any contact at all, it was very minimal Photo: Lexy Ilsley
10. Iliman Ndiaye 6
Showed some promising moments early on and then doubled United's advantage with a poacher's goal that his strike partner Sharp would have been proud of, heading home in front of the Kop. Did his best late on to prevent Blackpool running down the clock Photo: Simon Bellis
11. Billy Sharp 5
After an unselfish pass for Doyle which was ruled out, Sharp showed both his experience and selflessness to knock Doyle's cross down for the onrushing McAtee to score his first senior goal in front of the Kop. Saw a couple of efforts saved before making way for Brewster Photo: Isaac Parkin
12. Subs: Rhian Brewster 3
Good run down the left saw Ekpiteta see red - literally - after scything him down. Had the chance to earn a point for the Blades with two minutes left but his well-struck penalty hit the post and bounced clear after a stuttering run-up. Photo: Andrew Yates