Brazilian midfielder Gustavo Hamer’s trademark low-range drive had given the home side the lead early in the first half.
The Swans, though, would equalise minutes later from the spot with Championship top-scorer Zan Vipotnik slotting home his 18th of the season after Goncalo Franco had been brought down in the box by home goalkeeper Adam Davies.
Chances would be aplenty at either end, with Swans midfielder Melker Widell coming his effort cleared off the line by Blades defender Tyler Bindon, whilst both Hamer and forward Patrick Bamford would come close for United.
It would be the Blades, though, who would take control of the contest after the break, with Harrison Burrows assured finish regaining the lead.
Substitute Tom Cannon extended United advantage with an excellent curling effort from 25 yards, but the Swans would not lie down and battled back.
Former Celtic forward Idah proving to be the difference-maker on the day, netting his first strike since a three-month lay-off with a hamstring injury, coolly slotting fellow substitute Jay Fulton’s pull-back.
The Republic of Ireland international would then turn provider, showing good tenacity out wide to find South Korean forward Eom-Ji Sung to dramatically level from close-range to earn Swansea a point.
Neither side could force a winner from an entertaining end-of-season contest. Despite their comeback, Vitor Matos’ side drop to 16th in the table, while Sheffield United remain 17th.
Swansea welcome promotion-chasing Middlesbrough to the Swansea.com Stadium in their next fixture on Easter Monday in a slightly later kick-off of 530pm.
Swansea City X1:
Lawrence Vigouroux, Joel Ward, Ben Cabango (captain), Cameron Burgess, Josh Tymon; Marko Stamenic (Jay Fulton 70), Goncalo Franco, Malick Yalcouye (Liam Cullen 58); Ronald (Gustavo Nunes 58), Melker Widell (Jisung Eom 76), Zan Vipotnik (Adam Idah 70).
[Lead image: Swansea City FC]
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